Author name cluster

Nicolas Mansard

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54 papers

1 author row

ICRA Conference 2025 Conference Paper

Collision Avoidance in Model Predictive Control Using Velocity Damper

Arthur Haffemayer
Armand Jordana
Ludovic De Matteïs
Krzysztof Wojciechowski
Ludovic Righetti
Florent Lamiraux
Nicolas Mansard

We propose an advanced method for controlling the motion of a manipulator robot with strict collision avoidance in dynamic environments, leveraging a velocity damper constraint. Unlike conventional distance-based constraints, which tend to saturate near obstacles to reach optimality, the velocity damper constraint considers both distance and relative velocity, ensuring a safer separation. This constraint is incorporated into a model predictive control framework and enforced as a hard constraint through analytical derivatives supplied to the numerical solver. The approach has been fully implemented on a Franka Emika Panda robot and validated through experimental trials, demonstrating effective collision avoidance during dynamic tasks and robustness to unmodeled disturbances. An efficient open-source implementation along examples are provided here: https://gepettoweb.laas.fr/articles/haffemayer2025.html.

IROS Conference 2025 Conference Paper

Optimal Control of Walkers with Parallel Actuation

Ludovic De Matteïs
Virgile Batto
Justin Carpentier
Nicolas Mansard

Legged robots with closed-loop kinematic chains are increasingly prevalent due to their increased mobility and efficiency. Yet, most motion generation methods rely on serial-chain approximations, sidestepping their specific constraints and dynamics. This leads to suboptimal motions and limits the adaptability of these methods to diverse kinematic structures. We propose a comprehensive motion generation method that explicitly incorporates closed-loop kinematics and their associated constraints in an optimal control problem (OCP), integrating kinematic closure conditions and their analytical derivatives. This allows the solver to leverage the non-linear transmission effects inherent to closed-chain mechanisms, reducing peak actuator efforts and expanding their effective operating range. Unlike previous methods, our framework does not require serial approximations, enabling more accurate and efficient motion strategies. We also are able to generate the motion of more complex robots for which an approximate serial chain does not exist. We validate our approach through simulations and experiments, demonstrating superior performance in complex tasks such as rapid locomotion and stair negotiation. This method enhances the capabilities of current closed-loop robots and broadens the design space for future kinematic architectures.

ICRA Conference 2025 Conference Paper

Optimizing Complex Control Systems with Differentiable Simulators: A Hybrid Approach to Reinforcement Learning and Trajectory Planning

Amit Parag
Nicolas Mansard
Ekrem Misimi

Deep reinforcement learning (RL) often relies on simulators as abstract oracles to model interactions within complex environments. While differentiable simulators have recently emerged for multi-body robotic systems, they remain underutilized, despite their potential to provide richer information. This underutilization, coupled with the high computational cost of exploration-exploitation in high-dimensional state spaces, limits the practical application of RL in the real-world. We propose a method that integrates learning with differentiable simulators to enhance the efficiency of exploration-exploitation. Our approach learns value functions, state trajectories, and control policies from locally optimal runs of a model-based trajectory optimizer. The learned value function acts as a proxy to shorten the preview horizon, while approximated state and control policies guide the trajectory optimization. We benchmark our algorithm on three classical control problems and a torque-controlled 7 degree-of-freedom robot manipulator arm, demonstrating faster convergence and a more efficient symbiotic relationship between learning and simulation for end-to-end training of complex, poly-articulated systems.

IROS Conference 2024 Conference Paper

CaT: Constraints as Terminations for Legged Locomotion Reinforcement Learning

Elliot Chane-Sane
Pierre-Alexandre Leziart
Thomas Flayols
Olivier Stasse
Philippe Souères
Nicolas Mansard

Deep Reinforcement Learning (RL) has demonstrated impressive results in solving complex robotic tasks such as quadruped locomotion. Yet, current solvers fail to produce efficient policies respecting hard constraints. In this work, we advocate for integrating constraints into robot learning and present Constraints as Terminations (CaT), a novel constrained RL algorithm. Departing from classical constrained RL formulations, we reformulate constraints through stochastic terminations during policy learning: any violation of a constraint triggers a probability of terminating potential future rewards the RL agent could attain. We propose an algorithmic approach to this formulation, by minimally modifying widely used off-the-shelf RL algorithms in robot learning (such as Proximal Policy Optimization). Our approach leads to excellent constraint adherence without introducing undue complexity and computational overhead, thus mitigating barriers to broader adoption. Through empirical evaluation on the real quadruped robot Solo crossing challenging obstacles, we demonstrate that CaT provides a compelling solution for incorporating constraints into RL frameworks. Videos and code are available at constraints-as-terminations.github.io.

ICRA Conference 2024 Conference Paper

Force Feedback Model-Predictive Control via Online Estimation

Armand Jordana
Sébastien Kleff
Justin Carpentier
Nicolas Mansard
Ludovic Righetti

Nonlinear model-predictive control has recently shown its practicability in robotics. However it remains limited in contact interaction tasks due to its inability to leverage sensed efforts. In this work, we propose a novel model-predictive control approach that incorporates direct feedback from force sensors while circumventing explicit modeling of the contact force evolution. Our approach is based on the online estimation of the discrepancy between the force predicted by the dynamics model and force measurements, combined with high-frequency nonlinear model-predictive control. We report an experimental validation on a torque-controlled manipulator in challenging tasks for which accurate force tracking is necessary. We show that a simple reformulation of the optimal control problem combined with standard estimation tools enables to achieve state-of-the-art performance in force control while preserving the benefits of model-predictive control, thereby outperforming traditional force control techniques. This work paves the way toward a more systematic integration of force sensors in model predictive control.

ICRA Conference 2023 Conference Paper

Multi-Contact Task and Motion Planning Guided by Video Demonstration

Kateryna Zorina
David Kovár
Florent Lamiraux
Nicolas Mansard
Justin Carpentier
Josef Sivic
Vladimír Petrík

This work aims at leveraging instructional video to guide the solving of complex multi-contact task-and-motion planning tasks in robotics. Towards this goal, we propose an extension of the well-established Rapidly-Exploring Random Tree (RRT) planner, which simultaneously grows multiple trees around grasp and release states extracted from the guiding video. Our key novelty lies in combining contact states, and 3D object poses extracted from the guiding video with a traditional planning algorithm that allows us to solve tasks with sequential dependencies, for example, if an object needs to be placed at a specific location to be grasped later. To demonstrate the benefits of the proposed video-guided planning approach, we design a new benchmark with three challenging tasks: (i) 3D re-arrangement of multiple objects between a table and a shelf, (ii) multi-contact transfer of an object through a tunnel, and (iii) transferring objects using a tray in a similar way a waiter transfers dishes. We demonstrate the effectiveness of our planning algorithm on several robots, including the Franka Emika Panda and the KUKA KMR iiwa.

IROS Conference 2023 Conference Paper

Multi-Modal Upper Limbs Human Motion Estimation from a Reduced Set of Affordable Sensors

Mohamed Adjel
Maxime Sabbah
Raphaël Dumas
Nicolas Mansard
Samer Mohammed
Bruno Watier
Vincent Bonnet

This study aims at developing a new affordable motion capture system for human upper limbs' joint kinematics estimation based on a reduced set of visual inertial measurement units coupled with a markerless skeleton tracking algorithm. The markerless skeleton tracking algorithm allows to alleviate the kinematic redundancy that is observed if only a single visual inertial measurement unit is used at the hand level but it introduces undesired outliers. A Sliding Window Inverse Kinematics Algoritm based on a biomechanical model is proposed to filter out outliers. It has the advantage to constrain the evolution of joint kinematics while being able to handle multi- modalities. The proposed system was validated with five healthy volunteers performing a popular rehabilitation pick and place task. Joint angles estimated using our method were compared with the ones obtained using a reference stereophotogrammetric system. The results showed an average root mean square error of 9. 7deg along with an average correlation of 0. 8. These results compare favorably with literature results obtained with more numerous and relatively costly sensors or more elaborated and expensive markerless systems.

IROS Conference 2022 Conference Paper

Constrained Differential Dynamic Programming: A primal-dual augmented Lagrangian approach

Wilson Jallet
Antoine Bambade
Nicolas Mansard
Justin Carpentier

Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver to iteratively compute its solution. On one hand, differential dynamic programming (DDP) provides an efficient approach to transcribe the optimal control problem into a finite-dimensional problem while optimally exploiting the sparsity induced by time. On the other hand, augmented Lagrangian methods make it possible to formulate efficient algorithms with advanced constraint-satisfaction strategies. In this paper, we propose to combine these two approaches into an efficient optimal control algorithm accepting both equality and inequality constraints. Based on the augmented Lagrangian literature, we first derive a generic primal-dual augmented Lagrangian strategy for nonlinear problems with equality and inequality constraints. We then apply it to the dynamic programming principle to solve the value-greedy optimization problems inherent to the backward pass of DDP, which we combine with a dedicated globalization strategy, resulting in a Newton-like algorithm for solving constrained trajectory optimization problems. Contrary to previous attempts of formu-lating an augmented Lagrangian version of DDP, our approach exhibits adequate convergence properties without any switch in strategies. We empirically demonstrate its interest with several case-studies from the robotics literature.

ICRA Conference 2022 Conference Paper

Implicit Differential Dynamic Programming

Wilson Jallet
Nicolas Mansard
Justin Carpentier

Over the past decade, the Differential Dynamic Programming (DDP) method has gained in maturity and popularity within the robotics community. Several recent contributions have led to the integration of constraints within the original DDP formulation, hence enlarging its domain of application while making it a strong and easy-to-implement competitor against alternative methods of the state of the art such as collocation or multiple-shooting approaches. Yet, and similarly to its competitors, DDP remains unable to cope with high-dimensional dynamics within a receding horizon fashion, such as in the case of online generation of athletic motion on humanoid robots. In this paper, we propose to make a step towards this objective by reformulating classical DDP as an implicit optimal control problem, allowing the use of more advanced integration schemes such as implicit or variational integrators. To that end, we introduce a primal-dual proximal Lagrangian approach capable of handling dynamical and path constraints in a unified manner, while taking advantage of the time sparsity inherent to optimal control problems. We show that this reformulation enables us to relax the dynamics along the optimization process by solving it inexactly: far from the optimality conditions, the dynamics are only partially fulfilled, but continuously enforced as the solver gets closer to the local optimal solution. This inexactness enables our approach to robustly handle large time steps (100 ms or more), unlike other DDP solvers of the state of the art, as experimentally validated through different robotic scenarii.

IROS Conference 2022 Conference Paper

Introducing Force Feedback in Model Predictive Control

Sébastien Kleff
Ewen Dantec
Guilhem Saurel
Nicolas Mansard
Ludovic Righetti

In the literature about model predictive control (MPC), contact forces are planned rather than controlled. In this paper, we propose a novel paradigm to incorporate effort measurements into a predictive controller, hence allowing to control them by direct measurement feedback. We first demonstrate why the classical optimal control formulation, based on position and velocity state feedback, cannot handle direct feedback on force information. Following previous approaches in force control, we then propose to augment the classical formulations with a model of the robot actuation, which naturally allows to generate online trajectories that adapt to sensed position, velocity and torques. We propose a complete implementation of this idea on the upper part of a real humanoid robot, and show through hardware experiments that this new formulation incorporating effort feedback outperforms classical MPC in challenging tasks where physical interaction with the environment is crucial.

IROS Conference 2022 Conference Paper

Real-time Footstep Planning and Control of the Solo Quadruped Robot in 3D Environments

Fanny Risbourg
Thomas Corbères
Pierre-Alexandre Leziart
Thomas Flayols
Nicolas Mansard
Steve Tonneau

Quadruped robots have proved their robustness to cross complex terrain despite little environment knowledge. Yet advanced locomotion controllers are expected to take advantage of exteroceptive information. This paper presents a complete method to plan and control the locomotion of quadruped robots when 3D information about the surrounding obstacles is available, based on several stages of decision. We first propose a contact planner formulated as a mixed-integer program, optimized on-line at each new robot step. It selects a surface from a set of convex surfaces describing the environment for the next footsteps while ensuring kinematic constraints. We then propose to optimize the exact contact location and the feet trajectories at control frequency to avoid obstacles, thanks to an efficient formulation of quadratic programs optimizing Bezier curves. By relying on the locomotion controller of our quadruped robot Solo, we finally implement the complete method, provided as an open-source package. Its efficiency is asserted by statistical evaluation of the importance of each component in simulation. We have a 100% success rate for our framework, and we show that the deactivation of the contact planning, footstep adaptation and collision avoidance, respectively induced a drop to 70%, 62% and 83% success rate in the worst case, justifying the complete architecture.

ICRA Conference 2022 Conference Paper

Value learning from trajectory optimization and Sobolev descent: A step toward reinforcement learning with superlinear convergence properties

Amit Parag
Sébastien Kleff
Léo Saci
Nicolas Mansard
Olivier Stasse

The recent successes in deep reinforcement learning largely rely on the capabilities of generating masses of data, which in turn implies the use of a simulator. In particular, current progress in multi body dynamic simulators are under-pinning the implementation of reinforcement learning for end-to-end control of robotic systems. Yet simulators are mostly considered as black boxes while we have the knowledge to make them produce a richer information. In this paper, we are proposing to use the derivatives of the simulator to help with the convergence of the learning. For that, we combine model-based trajectory optimization to produce informative trials using 1st- and 2nd-order simulation derivatives. These locally-optimal runs give fair estimates of the value function and its derivatives, that we use to accelerate the convergence of the critics using Sobolev learning. We empirically demonstrate that the algorithm leads to a faster and more accurate estimation of the value function. The resulting value estimate is used in model-predictive controller as a proxy for shortening the preview horizon. We believe that it is also a first step toward superlinear reinforcement learning algorithm using simulation derivatives, that we need for end-to-end legged locomotion.

ICRA Conference 2021 Conference Paper

A Hybrid Collision Model for Safety Collision Control

Thibault Noël
Thomas Flayols
Joseph Mirabel
Justin Carpentier
Nicolas Mansard

Self-collision detection and avoidance are essential for reactive control, in particular for dynamics robots equipped with legs or arms. Yet, only few control methods are able to handle such constraints, and it is often necessary to rely on path planning to define a collision-free trajectory that the controller would then track. In this paper, we introduce a combination of two lightweight, conservative and smooth models to generically handle self-collisions in robot control. For pairs of bodies that are far from one another on average (e. g. segments of distinct legs), we rely on a standard forward kinematics approach, using simplified geometries for which we provide analytical derivatives. For bodies that are moving close to one another, we propose to use a data-driven approach, with datasets generated thanks to a standard collision library. We then build a simple torque-based controller that can be implemented on top of any control law to prevent unexpected self-collision. This controller is meant to be implemented as a low-level protection, directly on the robot hardware. We also provide an open-source library to generate ANSI-C code for any robot model, experimented on the real quadruped Solo.

ICRA Conference 2021 Conference Paper

Comparison of predictive controllers for locomotion and balance recovery of quadruped robots

Thomas Corbères
Thomas Flayols
Pierre-Alexandre Leziart
Rohan Budhiraja
Philippe Souères
Guilhem Saurel
Nicolas Mansard

As locomotion decisions must be taken by considering the future, most existing quadruped controllers are based on a model predictive controller (MPC) with a reduced model of the dynamics to generate the motion and a whole- body controller to execute it. Yet the simplifying assumptions of the MPC are often chosen ad-hoc or by intuition. In this article, we focus on a set of MPCs and analyze the effect of chosen model reductions on the behavior of the robot. Based on existing formulations, we present additional controllers to better understand the influence of model reductions on the controller capabilities. Finally, we propose a robust predictive controller capable of optimizing the foot placements, gait period, center- of-mass trajectory and ground reaction forces. The behavior of these controllers is statistically evaluated in simulation. This empirical study aims to assess the relative importance of the components of the optimal control problem (variables, costs, dynamics) to be able to take reasoned decisions instead of arbitrarily emphasizing or neglecting some of them. We also provide a qualitative study in simulation and on the real robot Solo-12.

ICRA Conference 2021 Conference Paper

Computational design of energy-efficient legged robots: Optimizing for size and actuators

Gabriele Fadini
Thomas Flayols
Andrea Del Prete
Nicolas Mansard
Philippe Souères

This paper presents a computational framework for the design of high-performance legged robotic systems. The framework relies on the concurrent optimization of hardware parameters and control trajectories to find the best robot design for a given task. In particular, we focus on energy efficiency, presenting novel electro-mechanical models to account for the losses of the actuators due to friction and Joule effects. Thanks to a bi-level optimization scheme, featuring a genetic algorithm in the outer loop, our framework can also optimize for the duration of the motion, the actuators, and the size of the robot. We present a novel approach to scale both the actuators and the robot structure in a way that ensures structural integrity by maintaining constant the normalized deflection of the links. We validated our approach by designing a two-joint monoped robot to execute a jumping task. Our simulation results show that our framework can lead to remarkable energy savings (up to 60%) thanks to the concurrent optimization of robot size, motion duration, and actuators.

ICRA Conference 2021 Conference Paper

Contact Forces Preintegration for Estimation in Legged Robotics using Factor Graphs

Médéric Fourmy
Thomas Flayols
Pierre-Alexandre Leziart
Nicolas Mansard
Joan Solà

State estimation, in particular estimation of the base position, orientation and velocity, plays a big role in the efficiency of legged robot stabilization. The estimation of the base state is particularly important because of its strong correlation with the underactuated dynamics, i. e. the evolution of center of mass and angular momentum. Yet this estimation is typically done in two phases, first estimating the base state, then reconstructing the center of mass from the robot model. The underactuated dynamics is indeed not properly observed, and any bias in the model would not be corrected from the sensors. While it has already been observed that force measurements make such a bias observable, these are often only used for a binary estimation of the contact state. In this paper, we propose to simultaneously estimate the base and the underactuation state by exploiting all measurements simultaneously. To this end, we propose several contributions to implement a complete state estimator using factor graphs. Contact forces altering the underactuated dynamics are pre-integrated using a novel adaptation of the IMU pre-integration method, which constitutes the principal contribution. IMU pre-integration is also used to estimate the positional motion of the base. Encoder measurements then participate to the estimation in two ways: by providing leg odometry displacements which contributes to the observability of IMU biases; and by relating the positional and centroidal states, thus connecting the whole graph and producing a tightly-coupled whole-body estimator. The validity of the approach is demonstrated on real data captured by the Solo12 quadruped robot.

ICRA Conference 2021 Conference Paper

High-Frequency Nonlinear Model Predictive Control of a Manipulator

Sébastien Kleff
Avadesh Meduri
Rohan Budhiraja
Nicolas Mansard
Ludovic Righetti

Model Predictive Control (MPC) promises to endow robots with enough reactivity to perform complex tasks in dynamic environments by frequently updating their motion plan based on measurements. Despite its appeal, it has seldom been deployed on real machines because of scaling constraints. This paper presents the first hardware implementation of closed-loop nonlinear MPC on a 7-DoF torque-controlled robot. Our controller leverages a state-of-the art optimal control solver, namely Differential Dynamic Programming (DDP), in order to replan state and control trajectories at real-time rates (1kHz). In addition to this experimental proof of concept, an exhaustive performance analysis shows that our controller outperforms open-loop MPC on a rapid cyclic end-effector task. We also exhibit the importance of a sufficient preview horizon and full robot dynamics through comparisons with inverse dynamics and kinematic optimization.

ICRA Conference 2021 Conference Paper

Implementation of a Reactive Walking Controller for the New Open-Hardware Quadruped Solo-12

Pierre-Alexandre Leziart
Thomas Flayols
Felix Grimminger
Nicolas Mansard
Philippe Souères

This paper aims at showing the dynamic performance and reliability of the low-cost, open-access quadruped robot Solo-12, which is developed within the framework of Open Dynamic Robot Initiative. It presents the implementation of a state-of-the-art control pipeline, close to the one that was previously implemented on Mini Cheetah, which implements a model predictive controller based on the centroidal dynamics to compute desired contact forces in order to track a reference velocity. Different contributions are proposed to speed up the computation process, notably at the level of the state estimation and the whole body controller. Experimental results demonstrate that the robot closely follow the reference velocity while being highly reactive and able to recover from perturbations.

ICRA Conference 2021 Conference Paper

Learning to steer a locomotion contact planner

Jason Chemin
Pierre Fernbach
Daeun Song
Guilhem Saurel
Nicolas Mansard
Steve Tonneau

The combinatorics inherent to the issue of planning legged locomotion can be addressed by decomposing the problem: first, select a guide path abstracting the contacts with a heuristic model; then compute the contact sequence to balance the robot gait along the guide path. While several models have been proposed to compute such a path, none have yet managed to efficiently capture the complexity of legged locomotion on arbitrary terrain. In this paper, we present a novel method to automatically build a local controller, or steering method, to generate a guide path along which a feasible contact sequence can be built. Our reinforcement learning approach is coupled with a geometric condition for feasibility during the training, which improves the convergence rate without incurring a loss in generality. We have designed a dedicated environment along with an associated reward function to run a classical reinforcement learning algorithm that computes the steering method. The policy takes a target velocity and a local heightmap of the terrain around the robot as inputs, and steers the path where new contacts should be created. It is then coupled with a contact generator that creates the contacts to support the robot movement. We show that the trained policy has an improved generalization and higher success rate at generating feasible contact plans than previous approaches. As a result, this policy can be used with a path planning algorithm to navigate complex environments.

ICRA Conference 2021 Conference Paper

Whole Body Model Predictive Control with a Memory of Motion: Experiments on a Torque-Controlled Talos

Ewen Dantec
Rohan Budhiraja
Adria Roig
Teguh Santoso Lembono
Guilhem Saurel
Olivier Stasse
Pierre Fernbach
Steve Tonneau

This paper presents the first successful experiment implementing whole-body model predictive control with state feedback on a torque-control humanoid robot. We demonstrate that our control scheme is able to do whole-body target tracking, control the balance in front of strong external perturbations and avoid collision with an external object. The key elements for this success are threefold. First, optimal control over a receding horizon is implemented with Crocoddyl, an optimal control library based on differential dynamics programming, providing state-feedback control in less than 10 ms. Second, a warm start strategy based on memory of motion has been implemented to overcome the sensitivity of the optimal control solver to initial conditions. Finally, the optimal trajectories are executed by a low-level torque controller, feedbacking on direct torque measurement at high frequency. This paper provides the details of the method, along with analytical benchmarks with the real humanoid robot Talos. A video of the experiment is available at https://peertube.laas.fr/videos/watch/cbc25927-337c-4635-a1bc-153b9aeb4135

ICRA Conference 2020 Conference Paper

Crocoddyl: An Efficient and Versatile Framework for Multi-Contact Optimal Control

Carlos Mastalli
Rohan Budhiraja
Wolfgang Merkt
Guilhem Saurel
Bilal Hammoud
Maximilien Naveau
Justin Carpentier
Ludovic Righetti

We introduce Crocoddyl (Contact RObot COntrol by Differential DYnamic Library), an open-source framework tailored for efficient multi-contact optimal control. Crocoddyl efficiently computes the state trajectory and the control policy for a given predefined sequence of contacts. Its efficiency is due to the use of sparse analytical derivatives, exploitation of the problem structure, and data sharing. It employs differential geometry to properly describe the state of any geometrical system, e. g. floating-base systems. Additionally, we propose a novel optimal control algorithm called Feasibility-driven Differential Dynamic Programming (FDDP). Our method does not add extra decision variables which often increases the computation time per iteration due to factorization. FDDP shows a greater globalization strategy compared to classical Differential Dynamic Programming (DDP) algorithms. Concretely, we propose two modifications to the classical DDP algorithm. First, the backward pass accepts infeasible state-control trajectories. Second, the rollout keeps the gaps open during the early "exploratory" iterations (as expected in multipleshooting methods with only equality constraints). We showcase the performance of our framework using different tasks. With our method, we can compute highly-dynamic maneuvers (e. g. jumping, front-flip) within few milliseconds.

ICRA Conference 2020 Conference Paper

Learning How to Walk: Warm-starting Optimal Control Solver with Memory of Motion

Teguh Santoso Lembono
Carlos Mastalli
Pierre Fernbach
Nicolas Mansard
Sylvain Calinon

In this paper, we propose a framework to build a memory of motion for warm-starting an optimal control solver for the locomotion task of a humanoid robot. We use HPP Loco3D, a versatile locomotion planner, to generate offline a set of dynamically consistent whole-body trajectory to be stored as the memory of motion. The learning problem is formulated as a regression problem to predict a single-step motion given the desired contact locations, which is used as a building block for producing multi-step motions. The predicted motion is then used as a warm-start for the fast optimal control solver Crocoddyl. We have shown that the approach manages to reduce the required number of iterations to reach the convergence from ~9. 5 to only ~3. 0 iterations for the single-step motion and from ~6. 2 to ~4. 5 iterations for the multi-step motion, while maintaining the solution's quality.

ICRA Conference 2020 Conference Paper

SL1M: Sparse L1-norm Minimization for contact planning on uneven terrain

Steve Tonneau
Daeun Song
Pierre Fernbach
Nicolas Mansard
Michel Taïx
Andrea Del Prete

One of the main challenges of planning legged locomotion in complex environments is the combinatorial contact selection problem. Recent contributions propose to use integer variables to represent which contact surface is selected, and then to rely on modern mixed-integer (MI) optimization solvers to handle this combinatorial issue. To reduce the computational cost of MI, we exploit the sparsity properties of L1 norm minimization techniques to relax the contact planning problem into a feasibility linear program. Our approach accounts for kinematic reachability of the center of mass (COM) and of the contact effectors. We ensure the existence of a quasi-static COM trajectory by restricting our plan to quasi-flat contacts. For planning 10 steps with less than 10 potential contact surfaces for each phase, our approach is 50 to 100 times faster that its MI counterpart, which suggests potential applications for online contact re-planning. The method is demonstrated in simulation with the humanoid robots HRP-2 and Talos over various scenarios.

ICRA Conference 2019 Conference Paper

Dynamics Consensus between Centroidal and Whole-Body Models for Locomotion of Legged Robots

Rohan Budhiraja
Justin Carpentier
Nicolas Mansard

It is nowadays well-established that locomotion can be written as a large and complex optimal control problem. Yet, current knowledge in numerical solver fails to directly solve it. A common approach is to cut the dimensionality by relying on reduced models (inverted pendulum, capture points, centroidal). However it is difficult both to account for whole-body constraints at the reduced level and also to define what is an acceptable trade-off at the whole-body level between tracking the reduced solution or searching for a new one. The main contribution of this paper is to introduce a rigorous mathematical framework based on the Alternating Direction Method of Multipliers, to enforce the consensus between the centroidal state dynamics at reduced and whole-body level. We propose an exact splitting of the whole-body optimal control problem between the centroidal dynamics (under-actuation) and the manipulator dynamics (full actuation), corresponding to a re-arrangement of the equations already stated in previous works. We then describe with details how alternating descent is a good solution to implement an effective locomotion solver. We validate this approach in simulation with walking experiments on the HRP-2 robot.

ICRA Conference 2018 Conference Paper

Using a Memory of Motion to Efficiently Warm-Start a Nonlinear Predictive Controller

Nicolas Mansard
A. DelPrete
Mathieu Geisert
Steve Tonneau
Olivier Stasse

Predictive control is an efficient model-based methodology to control complex dynamical systems. In general, it boils down to the resolution at each control cycle of a large nonlinear optimization problem. A critical issue is then to provide a good guess to initialize the nonlinear solver so as to speed up convergence. This is particularly important when disturbances or changes in the environment prevent the use of the trajectory computed at the previous control cycle as initial guess. In this paper, we introduce an original and very efficient solution to automatically build this initial guess. We propose to rely on off-line computation to build an approximation of the optimal trajectories, that can be used on-line to initialize the predictive controller. To that end, we combined the use of sampling-based planning, policy learning with generic representations (such as neural networks), and direct optimal control. We first propose an algorithm to simultaneously build a kinodynamic probabilistic roadmap (PRM) and approximate value function and control policy. This algorithm quickly converges toward an approximation of the optimal state-control trajectories (along with an optimal PRM). Then, we propose two methods to store the optimal trajectories and use them to initialize the predictive controller. We experimentally show that directly storing the state-control trajectories leads the predictive controller to quickly converges (2 to 5 iterations) toward the (global) optimal solution. The results are validated in simulation with an unmanned aerial vehicle (UAV) and other dynamical systems.

IROS Conference 2017 Conference Paper

Actuator design of compliant walkers via optimal control

Gabriele Buondonno
Justin Carpentier
Guilhem Saurel
Nicolas Mansard
Alessandro De Luca 0001
Jean-Paul Laumond

We present an optimization framework for the design and analysis of underactuated biped walkers, characterized by passive or actuated joints with rigid or non-negligible elastic actuation/transmission elements. The framework is based on optimal control, dealing with geometric constraints and various dynamic objective functions, as well as boundary conditions, which helps in selecting optimal values both for the actuation and the transmission parameters. Solutions of the formulated problems are shown for different kinds of bipedal architectures, and comparisons drawn between traditional rigid robots and compliant ones show the energy-efficiency of compliant actuators in the context of locomotion.

ICRA Conference 2016 Conference Paper

A versatile and efficient pattern generator for generalized legged locomotion

Justin Carpentier
Steve Tonneau
Maximilien Naveau
Olivier Stasse
Nicolas Mansard

This paper presents a generic and efficient approach to generate dynamically consistent motions for under-actuated systems like humanoid or quadruped robots. The main contribution is a walking pattern generator, able to compute a stable trajectory of the center of mass of the robot along with the angular momentum, for any given configuration of contacts (e. g. on uneven, sloppy or slippery terrain, or with closed-gripper). Unlike existing methods, our solver is fast enough to be applied as a model-predictive controller. We then integrate this pattern generator in a complete framework: an acyclic contact planner is first used to automatically compute the contact sequence from a 3D model of the environment and a desired final posture; a stable walking pattern is then computed by the proposed solver; a dynamically-stable whole-body trajectory is finally obtained using a second-order hierarchical inverse kinematics. The implementation of the whole pipeline is fast enough to plan a step while the previous one is executed. The interest of the method is demonstrated by real experiments on the HRP-2 robot, by performing long-step walking and climbing a staircase with handrail support.

ICRA Conference 2016 Conference Paper

Fast algorithms to test robust static equilibrium for legged robots

Andrea Del Prete
Steve Tonneau
Nicolas Mansard

Maintaining equilibrium is of primary importance for legged systems. It is not surprising then that static equilibrium is at the core of most control/planning algorithms for legged robots. Being able to check whether a system is in static equilibrium is thus important, and doing it efficiently is crucial. While this is straightforward for a system in contact with a flat ground only, it is not the case for arbitrary contact geometries. In this paper we propose two new techniques to test static equilibrium and we show that they are computationally faster than all other existing methods. Moreover, we address the issue of robustness to errors in the contact-force tracking, which could lead to slippage or rotation at the contacts. We extend all the discussed techniques to test for robust static equilibrium, that is the ability to maintain equilibrium while avoiding to lose contacts despite bounded force-tracking errors. Accounting for robustness does not affect the computation time of the equilibrium tests, while it qualitatively improves the contact postures generated by our reachability-based multicontact planner.

IROS Conference 2016 Conference Paper

HPP: A new software for constrained motion planning

Joseph Mirabel
Steve Tonneau
Pierre Fernbach
Anna-Kaarina Seppala
Mylène Campana
Nicolas Mansard
Florent Lamiraux

We present HPP, a software designed for complex classes of motion planning problems, such as navigation among movable objects, manipulation, contact-rich multiped locomotion, or elastic rods in cluttered environments. HPP is an open-source answer to the lack of a standard framework for these important issues for robotics and graphics communities.

ICRA Conference 2016 Conference Paper

Trajectory generation for quadrotor based systems using numerical optimal control

Mathieu Geisert
Nicolas Mansard

The recent work on quadrotor have focused on more and more challenging tasks with increasingly complex systems. Systems are often augmented with slung loads, inverted pendulums or arms, and accomplish complex tasks such as going through a window, grasping, throwing and catching. Usually, controllers are designed to accomplish a specific task on a specific system using analytic solutions, so each application needs long preparations. On the other hand, the direct multiple shooting approach is able to solve complex problems without any analytic development, by using off-the-shelf optimization solver. In this paper, we show that this approach is able to solve a wide range of problems relevant to quadrotor systems, from on-line trajectory generation for quadrotors to going through a window for a quadrotor-and-pendulum system, through manipulation tasks for a aerial manipulator.

ICRA Conference 2015 Conference Paper

Prioritized optimal control: A hierarchical differential dynamic programming approach

Francesco Romano
Andrea Del Prete
Nicolas Mansard
Francesco Nori

This paper deals with the generation of motion for complex dynamical systems (such as humanoid robots) to achieve several concurrent objectives. Hierarchy of tasks and optimal control are two frameworks commonly used to this aim. The first one specifies control objectives as a number of quadratic functions to be minimized under strict priorities. The second one minimizes an arbitrary user-defined function of the future state of the system, thus considering its evolution in time. Our recent work on prioritized optimal control merges the advantages of both these methods. This paper reformulates the original prioritized optimal control algorithm with the precise goal of improving its computational speed. We extend the dynamic programming method to work with a hierarchy of tasks. We compared our approach in simulation with both our previous algorithm and classical optimal control. The measured computational improvement represents another step towards the application of prioritized optimal control for online model predictive control of humanoid robots. We believe that this could be the key to unlock the (so far unexploited) dynamic capabilities of these mechanical systems.

IROS Conference 2015 Conference Paper

Whole-body model-predictive control applied to the HRP-2 humanoid

Jonas Koenemann
Andrea Del Prete
Yuval Tassa
Emanuel Todorov
Olivier Stasse
Maren Bennewitz
Nicolas Mansard

Controlling the robot with a permanently-updated optimal trajectory, also known as model predictive control, is the Holy Grail of whole-body motion generation. Before obtaining it, several challenges should be faced: computation cost, non-linear local minima, algorithm stability, etc. In this paper, we address the problem of applying the updated optimal control in real-time on the physical robot. In particular, we focus on the problems raised by the delays due to computation and by the differences between the real robot and the simulated model. Based on the optimal-control solver MuJoCo, we implemented a complete model-predictive controller and we applied it in real-time on the physical HRP-2 robot. It is the first time that such a whole-body model predictive controller is applied in real-time on a complex dynamic robot. Aside from the technical contributions cited above, the main contribution of this paper is to report the experimental results of this première implementation.

ICRA Conference 2014 Conference Paper

Control-limited differential dynamic programming

Yuval Tassa
Nicolas Mansard
Emanuel Todorov

Trajectory optimizers are a powerful class of methods for generating goal-directed robot motion. Differential Dynamic Programming (DDP) is an indirect method which optimizes only over the unconstrained control-space and is therefore fast enough to allow real-time control of a full humanoid robot on modern computers. Although indirect methods automatically take into account state constraints, control limits pose a difficulty. This is particularly problematic when an expensive robot is strong enough to break itself. In this paper, we demonstrate that simple heuristics used to enforce limits (clamping and penalizing) are not efficient in general. We then propose a generalization of DDP which accommodates box inequality constraints on the controls, without significantly sacrificing convergence quality or computational effort. We apply our algorithm to three simulated problems, including the 36-DoF HRP-2 robot. A movie of our results can be found here goo. gl/eeiMnn.

IROS Conference 2014 Conference Paper

Partial force control of constrained floating-base robots

Andrea Del Prete
Nicolas Mansard
Francesco Nori
Giorgio Metta
Lorenzo Natale

Legged robots are typically in rigid contact with the environment at multiple locations, which add a degree of complexity to their control. We present a method to control the motion and a subset of the contact forces of a floating-base robot. We derive a new formulation of the lexicographic optimization problem typically arising in multi-task motion/force control frameworks. The structure of the constraints of the problem (i. e. the dynamics of the robot) allows us to find a sparse analytical solution. This leads to an equivalent optimization with reduced computational complexity, comparable to inverse-dynamics based approaches. At the same time, our method preserves the flexibility of optimization based control frameworks. Simulations were carried out to achieve different multi-contact behaviors on a 23-degree-of-freedom humanoid robot, validating the presented approach. A comparison with another state-of-the-art control technique with similar computational complexity shows the benefits of our controller, which can eliminate force/torque discontinuities.

ICRA Conference 2012 Conference Paper

A dedicated solver for fast operational-space inverse dynamics

Nicolas Mansard

The most classical solution to generate whole-body motions on humanoid robots is to use the inverse kinematics on a set of tasks. It enables flexibility, repeatability, sensor-feedback if needed, and can be applied in real time onboard the robot. However, it cannot comprehend the whole complexity of the robot dynamics. Inverse dynamics is then a mandatory evolution. Before application as a generic motion generator, two important concerns need to be solved. First, when including in the motion-generation problem the forces and torques variables, the numerical conditioning can become very low, inducing undesired behaviors or even divergence. Second, the computational costs of the problem resolution is much more important than when considering the kinematics alone. This paper proposes a complete reformulation of the inverse-dynamics problem, by cutting the ill-conditioned part of the problem, solving in a same way the problem of numerical stability and of cost reduction. The approach is validated by a set of dynamic whole-body movements of the HRP-2 robot.

ICRA Conference 2012 Conference Paper

Capture, recognition and imitation of anthropomorphic motion

Sovannara Hak
Nicolas Mansard
Oscar E. Ramos
Layale Saab
Olivier Stasse

We presented our works relative to anthropomorphic motions. We performed task recognition, full-dynamic motion generation, motion retargeting and editing in a unified framework: the stack of tasks. Thanks to the genericity of the task function formalism, our works can be further extended. For example, for the recognition, the use of the task function formalism applied to human motion is currently investigated. Also, preliminary results on the real robot for the retargeting and editing method have been obtained.

IROS Conference 2011 Conference Paper

Analysis of the discontinuities in prioritized tasks-space control under discreet task scheduling operations

François Keith
Pierre-Brice Wieber
Nicolas Mansard
Abderrahmane Kheddar

This paper examines the control continuity in hierarchical task-space controllers. While the continuity is ensured for any a priori fixed number of tasks -even in ill-conditioned configurations-, the control resulting from a hierarchical stack-of-task computation may not be continuous under some discrete events. In particular, we study how the continuity of the stack-of-task control computation is affected under discreet scheduling operations such as on-the-fly priority switching between tasks, or tasks insertion and removal, which changes the number of tasks in the stack controller. Different ways to formulate a hierarchy of tasks are presented together with their continuity properties, which is thoroughly analyzed under such discreet scheduling operations.

ICRA Conference 2011 Conference Paper

Generation of dynamic motion for anthropomorphic systems under prioritized equality and inequality constraints

Layale Saab
Nicolas Mansard
François Keith
Jean-Yves Fourquet
Philippe Souères

In this paper, we propose a solution to compute full-dynamic motions for a humanoid robot, accounting for various kinds of constraints such as dynamic balance or joint limits. As a first step, we propose a unification of task-based control schemes, in inverse kinematics or inverse dynamics. Based on this unification, we generalize the cascade of quadratic programs that were developed for inverse kinematics only. Then, we apply the solution to generate, in simulation, whole-body motions for a humanoid robot in unilateral contact with the ground, while ensuring the dynamic balance on a non horizontal surface.

IROS Conference 2011 Conference Paper

Generic dynamic motion generation with multiple unilateral constraints

Layale Saab
Oscar E. Ramos
Nicolas Mansard
Philippe Souères
Jean-Yves Fourquet

Control methods based on a hierarchy of tasks provide a fast, easily-modifiable, and accurate way of generating a motion. In this paper, we propose to extend this hierarchical approach by using a cascade of quadratic programs to handle simultaneously the robot dynamics, inequality and equality constraints, and multiple non-coplanar unilateral contacts. First, we detail the proposed generic inverse-dynamics solver. Then, we prove that the model used to handle contacts encompasses the classical zero-moment-point balance condition. Finally, as an example of the capabilities of the method, we generate a complex motion where the humanoid robot HRP2 sits down on an armchair, using the armrests as additional contacts, while ensuring joint position and velocity limits.

ICRA Conference 2011 Conference Paper

Intermediate desired value approach for continuous transition among multiple tasks of robots

Jaemin Lee
Nicolas Mansard
Jaeheung Park

As the capability of robots is getting improved, more various tasks are expected to be performed by the robots. Complex operation of the robots can be composed of many different tasks. These tasks are executed sequentially, simultaneously, or in a combined way of both. This paper discusses the transition issue among multiple tasks on how the transition can be effectively and smoothly achieved. The proposed approach is to compose intermediate desired values to smooth the transitions rather than to modify control laws. The approach can be practically used on robotic systems without modification on their specific control algorithms. In this paper, multi-points control and joint limit avoidance are performed as applications of the proposed approach.

IROS Conference 2010 Conference Paper

Combining suppression of the disturbance and reactive stepping for recovering balance

Mitsuharu Morisawa
Fumio Kanehiro
Kenji Kaneko
Nicolas Mansard
Joan Solà
Eiichi Yoshida
Kazuhito Yokoi
Jean-Paul Laumond

This paper proposes a new framework to recover balance against external forces by combining disturbance suppression and reactive stepping. In the view point of the feedback control, a reactive step can help to diminish the disturbance caused by an external force that should be compensated to maintain balance. In other words, if the adequate step is performed, the feedback controller does not have to compensate all of the external force by itself. Under this concept, we propose an original solution to distribute the compensation between a feedback controller and a reactive step, according to the period of support phase and a disturbance characteristic. We first clearly distinguish between the role of the disturbance suppression and the reactive stepping. Then, based on this distinction, the small disturbance of external force or happening late during the single-support phase, is mainly suppressed by state feedback. The large disturbance which is out of capability by feedback controller and at the beginning of the single-support phase, is absorbed by modifying reactively the next steps. The proposed method is validated through experimental results with the HRP-2 humanoid robot.

ICRA Conference 2010 Conference Paper

Fast resolution of hierarchized inverse kinematics with inequality constraints

Adrien Escande
Nicolas Mansard
Pierre-Brice Wieber

Classically, the inverse kinematics is performed by computing the singular value decomposition of the matrix to invert. This enables a very simple writing of the algorithm. However, the computation cost is high, especially when applied to complex robots and complex sets of constraints (typically around 5ms for 50 degrees of freedom - DOF). In this paper, we propose a dedicated adaptation of quadratic programming that enables fast computations of the hierarchical inverse kinematics (around 0. 1ms for 50 DOF). We then extend this algorithm to deal with unilateral constraints, obtaining sufficiently high performances for reactive control.

ICAPS Conference 2009 Conference Paper

From Discrete Mission Schedule to Continuous Implicit Trajectory using Optimal Time Warping

François Keith
Nicolas Mansard
Sylvain Miossec
Abderrahmane Kheddar

This paper presents a generic solution to apply a mission described by a sequence of tasks on a robot while accounting for its physical constraints, without computing explicitly a reference trajectory. A naive solution to this problem would be to schedule the execution of the tasks sequentially, avoiding concurrency. This solution does not exploit fully the robot capabilities such as redundancy and have poor performance in terms of execution time or energy. Our contribution is to determine the time-optimal realization of the mission taking into account robotic constraints that may be as complex as collision avoidance. Our approach achieves more than a simple scheduling; its originality lies in maintaining the task approach in the formulated optimization of the task sequencing problem. This theory is exemplified through a complete experiment on the real HRP-2 robot.

IROS Conference 2009 Conference Paper

Intercontinental, multimodal, wide-range tele-cooperation using a humanoid robot

Paul Evrard
Nicolas Mansard
Olivier Stasse
Abderrahmane Kheddar
Thomas Schauss
Carolina Weber
Angelika Peer
Martin Buss

This paper is the continuation of our previous work in intercontinental, collaborative teleoperation with a humanoid robot. Our new achievement consists in an extension of the former single-arm bilateral teleoperation setting to include bimanual manipulation and walking. A coupling scheme for simultaneous manipulation and locomotion is developed. Furthermore, a task-based control framework, including a force-based control for the arms as well as a walking pattern generation, is presented to realize stable whole-body motions of the highly redundant humanoid robot. Experiments have been performed to assess the proposed control scheme. They bring to light additional scientific challenges that remain in order to reach a smooth and natural telepresent collaboration.

IROS Conference 2009 Conference Paper

Optimization of tasks warping and scheduling for smooth sequencing of robotic actions

François Keith
Nicolas Mansard
Sylvain Miossec
Abderrahmane Kheddar

This paper presents a method for sequencing a set of robotic tasks in an optimal way. Tasks description and execution are based on the task-function approach, which enables to build complex whole-body behaviors from local control laws. A naive solution to this problem would be to schedule the execution of the tasks sequentially, avoiding concurrency. This solution does not exploit full robot capabilities such as redundancy and have poor performance in terms of execution time or energy. However, reasoning on concurrent tasks is difficult while accounting for all the physical constraints of the robot. Our contribution is to determine the time-optimal realization of the mission taking into account robotic constraints that may be as complex as collision avoidance. Our approach achieves more than a simple scheduling; its originality lies in maintaining the task approach in the formulated optimization of the task sequencing problem. This theory is exemplified through a complete experiment on the real HRP-2 robot.

ICRA Conference 2008 Conference Paper

Continuous control law from unilateral constraints

Nicolas Mansard
Oussama Khatib

The control approaches based on tasks, and particularly based on a hierarchy of tasks, enable to build complex behaviors with some nice properties of robustness and portability. However it is difficult to consider directly unilateral constraints in such a framework. Unilateral constraints presents some strong irregularities (in particular at the level of their derivative) that prevents the insertion of unilateral-based tasks at the high-priority level of a hierarchy. In this paper, we present an original method to generalize the hierarchy-based control schemes to take unilateral constraint into account at the top-priority level. We develop our method first at the kinematic level then directly at the dynamic level using the operational space. The method is then validated on a various set of robots by realizing a visual servoing under the constraint of joint limits.

ICRA Conference 2008 Conference Paper

Real-time (self)-collision avoidance task on a hrp-2 humanoid robot

Olivier Stasse
Adrien Escande
Nicolas Mansard
Sylvain Miossec
Paul Evrard
Abderrahmane Kheddar

This paper proposes a real-time implementation of collision and self-collision avoidance for robots. On the basis of a new proximity distance computation method which ensures having continuous gradient, a new controller in the velocity domain is proposed. The gradient continuity encompasses no jump in the generated command. Included in a stack of tasks architecture, this controller has been implemented on the humanoid platform HRP-2 and experienced in a grasping task while walking and avoiding collisions with the environment and auto-collisions.

ICRA Conference 2007 Conference Paper

Integrating Walking and Vision to Increase Humanoid Robot Autonomy

Olivier Stasse
Björn Verrelst
Andrew J. Davison
Nicolas Mansard
Bram Vanderborght
Claudia Esteves
François Saïdi
Kazuhito Yokoi

This video demonstrates our current investigation in developing autonomous behaviors for humanoid robots. Our main goals is to develop functionalities as much generic as possible in order to realize useful behaviors. More particularly this video demonstrates our current status on extending a popular Zero Momentum Problem (ZMP) preview control based pattern generator, and building some links between walking with vision.

ICRA Conference 2007 Conference Paper

Visually-Guided Grasping while Walking on a Humanoid Robot

Nicolas Mansard
Olivier Stasse
François Chaumette
Kazuhito Yokoi

In this paper, we apply a general framework for building complex whole-body control for highly redundant robot, and we propose to implement it for visually-guided grasping while walking on a humanoid robot. The key idea is to divide the control into several sensor-based control tasks that are simultaneously executed by a general structure called stack of tasks. This structure enables a very simple access for task sequencing, and can be used for task-level control. This framework was applied for a visual servoing task. The robot walks along a planed path, keeping the specified object in the middle of its field of view and finally, when it is close enough, the robot grasps the object while walking.

IROS Conference 2006 Conference Paper

A Qualitative Visual Servoing to ensure the Visibility Constraint

Anthony Remazeilles
Nicolas Mansard
François Chaumette

This paper describes an original control law called qualitative servoing. The particularity of this method is that no specific desired value is specified for the visual features involved in the control scheme. Indeed, visual features are only constrained to belong to a confident interval, which gives more flexibility to the system. While this formalism can be used for several types of visual features, it is used in this paper for improving the on-line control of the visibility of a target. The principle is to make a compromise between the classical positioning task and the visibility constraint. Experimental results obtained with a six degrees of freedom robot arm are presented, demonstrating the performance of the proposed method

IROS Conference 2006 Conference Paper

Jacobian Learning Methods for Tasks Sequencing in Visual Servoing

Nicolas Mansard
Manuel Lopes 0001
José Santos-Victor
François Chaumette

In this paper, the coupling between Jacobian learning and task sequencing through the redundancy approach is studied. It is well known that visual servoing is robust to modeling errors in the Jacobian matrices. This justifies why Jacobian estimation does not usually degrade the system convergence. However, we show that this is not true any more when the redundancy formalism is used. In this case the Jacobian matrix is also necessary to compute projection operators for task decomposition, which is quite sensitive to errors. We show that learning improves the servoing performance, when task sequencing is used. Conversely, sequencing improves the convergence of learning, especially for tasks involving several degrees of freedom. Eye-in-hand and eye-to-hand experiments have been performed on two robots with six degrees of freedom

IROS Conference 2005 Conference Paper

A new redundancy formalism for avoidance in visual servoing

Nicolas Mansard
François Chaumette

The paper presents a new approach to construct a control law that realizes a main task and simultaneously takes supplementary constraints into account. Classically, this is done by using the redundancy formalism. If the main task does not constrain all the motions of the robot, a secondary task can be achieved by using only the remaining degrees of freedom (DOF). We propose a new general method that frees up some of the DOF constrained by the main task in addition of the remaining DOF. The general idea is to enable the motions produced by the secondary control law that help the main task to be completed faster. The main advantage is to enhance the performance of the secondary task by enlarging the number of available DOF. In a formal framework, a projection operator is built which ensures that the secondary control law does not disturb the main task. A control law can be then easily computed from the two tasks considered. Experiments that implement and validate this approach are proposed. The visual servoing framework is used to position a 6-DOF robot while simultaneously avoiding occlusions and joint limits.

ICRA Conference 2005 Conference Paper

Visual Servoing Sequencing Able to Avoid Obstacles

Nicolas Mansard
François Chaumette

Classical visual servoing approaches tend to constrain all degrees of freedom (DOF) of the robot during the execution of a task. In this article a new approach is proposed. The key idea is to control the robot with a very under-constrained task when it is far from the desired position, and to incrementally constrain the global task by adding further tasks as the robot moves closer to the goal. As long as they are sufficient, the remaining DOF are used to avoid undesirable configurations, such as joint limits. Closer from the goal, when not enough DOF remain available for avoidance, an execution controller selects a task to be temporary removed from the applied tasks. The released DOF can then be used for the joint limits avoidance. A complete solution to implement this general idea is proposed. Experiments that prove the validity of the approach are also provided.

IROS Conference 2004 Conference Paper

Tasks sequencing for visual servoing

Nicolas Mansard
François Chaumette

Classical visual servoing approaches tend to constrain all degrees of freedom (DOF) of the robot during a task's execution. In this article a new approach is proposed. The key idea is to control the robot with a very under-constrained task when it is far of the desired position, and to incrementally constrain the global task by adding further tasks as the robot moves closer to the goal. A method is first proposed that stacks elementary tasks until the robot is fully constrained. To insure the continuity of the articular velocities when adding constraints, a new control law is then proposed. Experiments that prove the interest of the approach are also provided.