Author name cluster

Justin Carpentier

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

19 papers

2 author rows

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 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.

ICLR Conference 2024 Conference Paper

Leveraging augmented-Lagrangian techniques for differentiating over infeasible quadratic programs in machine learning

Antoine Bambade
Fabian Schramm
Adrien B. Taylor
Justin Carpentier

Optimization layers within neural network architectures have become increasingly popular for their ability to solve a wide range of machine learning tasks and to model domain-specific knowledge. However, designing optimization layers requires careful consideration as the underlying optimization problems might be infeasible during training. Motivated by applications in learning, control and robotics, this work focuses on convex quadratic programming (QP) layers. The specific structure of this type of optimization layer can be efficiently exploited for faster computations while still allowing rich modeling capabilities. We leverage primal-dual augmented Lagrangian techniques for computing derivatives of both feasible and infeasible QP solutions. More precisely, we propose a unified approach which tackles the differentiability of the closest feasible QP solutions in a classical $\ell_2$ sense. We then harness this approach to enrich the expressive capabilities of existing QP layers. More precisely, we show how differentiating through infeasible QPs during training enables to drive towards feasibility at test time a new range of QP layers. These layers notably demonstrate superior predictive performance in some conventional learning tasks. Additionally, we present alternative formulations that enhance numerical robustness, speed, and accuracy for training such layers. Along with these contributions, we provide an open-source C++ software package called QPLayer for differentiating feasible and infeasible convex QPs and which can be interfaced with modern learning frameworks.

ICRA Conference 2024 Conference Paper

Risk-Sensitive Extended Kalman Filter

Armand Jordana
Avadesh Meduri
Etienne Arlaud
Justin Carpentier
Ludovic Righetti

Designing robust algorithms in the face of estimation uncertainty is a challenging task. Indeed, controllers seldom consider estimation uncertainty and only rely on the most likely estimated state. Consequently, sudden changes in the environment or the robot’s dynamics can lead to catastrophic behaviors. Leveraging recent results in risk-sensitive optimal control, this paper presents a risk-sensitive Extended Kalman Filter that can adapt its estimation to the control objective, hence allowing safe output-feedback Model Predictive Control (MPC). By taking a pessimistic estimate of the value function resulting from the MPC controller, the filter provides increased robustness to the controller in phases of uncertainty as compared to a standard Extended Kalman Filter (EKF). The filter has the same computational complexity as an EKF and can be used for real-time control. The paper evaluates the risk-sensitive behavior of the proposed filter when used in a nonlinear MPC loop on a planar drone and industrial manipulator in simulation, as well as on an external force estimation task on a real quadruped robot. These experiments demonstrate the ability of the approach to significantly improve performance in face of uncertainties.

ICRA Conference 2023 Conference Paper

Differentiable Collision Detection: a Randomized Smoothing Approach

Louis Montaut
Quentin Le Lidec
Antoine Bambade
Vladimír Petrík
Josef Sivic
Justin Carpentier

Collision detection is an important component of many robotics applications, from robot control to simulation, including motion planning and estimation. While the seminal works on the topic date back to the 80s, it is only recently that the question of properly differentiating collision detection has emerged as a central issue, thanks notably to the ongoing and various efforts made by the scientific community around the topic of differentiable physics. Yet, very few solutions have been suggested so far, and only with a strong assumption on the nature of the shapes involved. In this work, we introduce a generic and efficient approach to compute the derivatives of collision detection for any pair of convex shapes, by notably leveraging randomized smoothing techniques which have shown to be particularly adapted to capture the derivatives of non-smooth problems. This approach is implemented in the HPP-FCL and Pinocchio ecosystems, and evaluated on classic datasets and problems of the robotics literature, demonstrating few micro-second timings to compute informative derivatives directly exploitable by many real robotic applications, including differentiable simulation.

ICRA Conference 2023 Conference Paper

Enforcing the consensus between Trajectory Optimization and Policy Learning for precise robot control

Quentin Le Lidec
Wilson Jallet
Ivan Laptev
Cordelia Schmid
Justin Carpentier

Reinforcement learning (RL) and trajectory opti-mization (TO) present strong complementary advantages. On one hand, RL approaches are able to learn global control policies directly from data, but generally require large sample sizes to properly converge towards feasible policies. On the other hand, TO methods are able to exploit gradient-based information extracted from simulators to quickly converge towards a locally optimal control trajectory which is only valid within the vicinity of the solution. Over the past decade, several approaches have aimed to adequately combine the two classes of methods in order to obtain the best of both worlds. Following on from this line of research, we propose several improvements on top of these approaches to learn global control policies quicker, notably by leveraging sensitivity information stemming from TO methods via Sobolev learning, and Augmented Lagrangian (AL) techniques to enforce the consensus between TO and policy learning. We evaluate the benefits of these improvements on various classical tasks in robotics through comparison with existing approaches in the literature.

IROS Conference 2023 Conference Paper

Investigations into Exploiting the Full Capabilities of a Series-Parallel Hybrid Humanoid Using Whole Body Trajectory Optimization

Melya Boukheddimi
Rohit Kumar
Shivesh Kumar
Justin Carpentier
Frank Kirchner

Trajectory optimization methods have become ubiquitous for the motion planning and control of underactuated robots for e. g. , quadrupeds, humanoids etc. While they have been extensively used in the case of serial or tree type robots, they are seldomly used for planning and control of robots with closed loops. Series-parallel hybrid topology is quite commonly used in the design of humanoid robots, but they are often neglected during trajectory optimization and the movements are computed for a serial abstraction of the system and then the solution is mapped to the actuator coordinates. As a consequence, the full capability of the robot cannot be exploited. This paper presents a case study of trajectory optimization for series-parallel hybrid robot by taking into account all the holonomic constraints imposed by the closed kinematic loops present in the system. We demonstrate the advantages of this consideration with a weightlifting task on RH5 Manus humanoid in both simulation and experiments.

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 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.

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.

NeurIPS Conference 2021 Conference Paper

Differentiable rendering with perturbed optimizers

Quentin Le Lidec
Ivan Laptev
Cordelia Schmid
Justin Carpentier

Reasoning about 3D scenes from their 2D image projections is one of the core problems in computer vision. Solutions to this inverse and ill-posed problem typically involve a search for models that best explain observed image data. Notably, images depend both on the properties of observed scenes and on the process of image formation. Hence, if optimization techniques should be used to explain images, it is crucial to design differentable functions for the projection of 3D scenes into images, also known as differentiable rendering. Previous approaches to differentiable rendering typically replace non-differentiable operations by smooth approximations, impacting the subsequent 3D estimation. In this paper, we take a more general approach and study differentiable renderers through the prism of randomized optimization and the related notion of perturbed optimizers. In particular, our work highlights the link between some well-known differentiable renderer formulations and randomly smoothed optimizers, and introduces differentiable perturbed renderers. We also propose a variance reduction mechanism to alleviate the computational burden inherent to perturbed optimizers and introduce an adaptive scheme to automatically adjust the smoothing parameters of the rendering process. We apply our method to 3D scene reconstruction and demonstrate its advantages on the tasks of 6D pose estimation and 3D mesh reconstruction. By providing informative gradients that can be used as a strong supervisory signal, we demonstrate the benefits of perturbed renderers to obtain more accurate solutions when compared to the state-of-the-art alternatives using smooth gradient approximations.

ICRA Conference 2021 Conference Paper

Equality Constrained Differential Dynamic Programming

Sarah El Kazdadi
Justin Carpentier
Jean Ponce

Trajectory optimization is an important tool in task-based robot motion planning, due to its generality and convergence guarantees under some mild conditions. It is often used as a post-processing operation to smooth out trajectories that are generated by probabilistic methods or to directly control the robot motion. Unconstrained trajectory optimization problems have been well studied, and are commonly solved using Differential Dynamic Programming methods that allow for fast convergence at a relatively low computational cost. In this paper, we propose an augmented Lagrangian approach that extends these ideas to equality-constrained trajectory optimization problems, while maintaining a balance between convergence speed and numerical stability. We illustrate our contributions on various standard robotic problems and highlights their benefits compared to standard approaches.

NeurIPS Conference 2021 Conference Paper

Online Learning and Control of Complex Dynamical Systems from Sensory Input

Oumayma Bounou
Jean Ponce
Justin Carpentier

Identifying an effective model of a dynamical system from sensory data and using it for future state prediction and control is challenging. Recent data-driven algorithms based on Koopman theory are a promising approach to this problem, but they typically never update the model once it has been identified from a relatively small set of observation, thus making long-term prediction and control difficult for realistic systems, in robotics or fluid mechanics for example. This paper introduces a novel method for learning an embedding of the state space with linear dynamics from sensory data. Unlike previous approaches, the dynamics model can be updated online and thus easily applied to systems with non-linear dynamics in the original configuration space. The proposed approach is evaluated empirically on several classical dynamical systems and sensory modalities, with good performance on long-term prediction and control.

ICRA Conference 2021 Conference Paper

Optimal Estimation of the Centroidal Dynamics of Legged Robots

François Bailly
Justin Carpentier
Philippe Souères

Estimating the centroidal dynamics of legged robots is crucial in the context of multi-contact locomotion of legged robots. In this paper, we formulate the estimation of centroidal dynamics as a maximum a posteriori problem and we use a differential dynamic programming approach for solving it. The soundness of the proposed approach is first validated on a simulated humanoid robot, where ground truth data is available, enabling error analysis, and then compared to other alternatives of the state of the art, namely an extend Kalman filter and a recursive complementary filter. The results demonstrate that, compared to other approaches, the proposed method reduces the estimation error on the centroidal state in addition to ensuring the dynamics consistency of the state trajectory. Finally, the effectiveness of the proposed method is illustrated on real measurements, obtained from walking experiments with the HRP-2 humanoid robot.

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 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.

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.