Author name cluster

Todd D. Murphey

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.

40 papers

1 author row

ICRA Conference 2025 Conference Paper

Data Augmentation for NeRFs in the Low Data Limit

Ayush Gaggar
Todd D. Murphey

Current methods based on Neural Radiance Fields fail in the low data limit, particularly when training on incomplete scene data. Prior works augment training data only in next-best-view applications, which lead to hallucinations and model collapse with sparse data. In contrast, we propose adding a set of views during training by rejection sampling from a posterior uncertainty distribution, generated by combining a volumetric uncertainty estimator with spatial coverage. We validate our results on partially observed scenes; on average, our method performs 39. 9% better with 87. 5% less variability across established scene reconstruction benchmarks, as compared to state of the art baselines. We further demonstrate that augmenting the training set by sampling from any distribution leads to better, more consistent scene reconstruction in sparse environments. This work is foundational for robotic tasks where augmenting a dataset with informative data is critical in resource-constrained, a priori unknown environments. Videos and source code are available at https://murpheylab.github.iollow-data-nerfl

ICRA Conference 2025 Conference Paper

Inverse Mixed Strategy Games with Generative Trajectory Models

Muchen Sun
Peter Trautman
Todd D. Murphey

Game-theoretic models are effective tools for modeling multi-agent interactions, especially when robots need to coordinate with humans. However, applying these models requires inferring their specifications from observed behaviors—a challenging task known as the inverse game problem. Existing inverse game approaches often struggle to account for behavioral uncertainty and measurement noise, and leverage both offline and online data. To address these limitations, we propose an inverse game method that integrates a generative trajectory model into a differentiable mixed-strategy game framework. By representing the mixed strategy with a conditional variational autoencoder (CVAE), our method can infer high-dimensional, multi-modal behavior distributions from noisy measurements while adapting in real-time to new observations. We extensively evaluate our method in a simulated navigation benchmark, where the observations are generated by an unknown game model. Despite the model mismatch, our method can infer Nash-optimal actions comparable to those of the ground-truth model and the oracle inverse game baseline, even in the presence of uncertain agent objectives and noisy measurements.

IROS Conference 2025 Conference Paper

Real-Time Reinforcement Learning for Dynamic Tasks with a Parallel Soft Robot

James Avtges
Jake Ketchum
Millicent Schlafly
Helena Young
Taekyoung Kim
Allison Pinosky
Ryan L. Truby
Todd D. Murphey

Closed-loop control remains an open challenge in soft robotics. The nonlinear responses of soft actuators under dynamic loading conditions limit the use of analytic models for soft robot control. Traditional methods of controlling soft robots underutilize their configuration spaces to avoid nonlinearity, hysteresis, large deformations, and the risk of actuator damage. Furthermore, episodic data-driven control approaches such as reinforcement learning (RL) are traditionally limited by sample efficiency and inconsistency across initializations. In this work, we demonstrate RL for reliably learning control policies for dynamic balancing tasks in real-time single-shot hardware deployments. We use a deformable Stewart platform constructed using parallel, 3D-printed soft actuators based on motorized handed shearing auxetic (HSA) structures. By introducing a curriculum learning approach based on expanding neighborhoods of a known equilibrium, we achieve reliable single-deployment balancing at arbitrary coordinates. In addition to benchmarking the performance of model-based and model-free methods, we demonstrate that in a single deployment, Maximum Diffusion RL is capable of learning dynamic balancing after half of the actuators are effectively disabled, by inducing buckling and by breaking actuators with bolt cutters. Training occurs with no prior data, in as fast as 15 minutes, with performance nearly identical to the fully-intact platform. Single-shot learning on hardware facilitates soft robotic systems reliably learning in the real world and will enable more diverse and capable soft robots.

ICRA Conference 2024 Conference Paper

Active Exploration for Real-Time Haptic Training

Jake Ketchum
Ahalya Prabhakar
Todd D. Murphey

Tactile perception is important for robotic systems that interact with the world through touch. Touch is an active sense in which tactile measurements depend on the contact properties of an interaction—e. g. , velocity, force, acceleration— as well as properties of the sensor and object under test. These dependencies make training tactile perceptual models challenging. Additionally, the effects of limited sensor life and the near-field nature of tactile sensors preclude the practical collection of exhaustive data sets even for fairly simple objects. Active learning provides a mechanism for focusing on only the most informative aspects of an object during data collection. Here we employ an active learning approach that uses a data-driven model’s entropy as an uncertainty measure and explore relative to that entropy conditioned on the sensor state variables. Using a coverage-based ergodic controller, we train perceptual models in near-real time. We demonstrate our approach using a biomimentic sensor, exploring "tactile scenes" composed of shapes, textures, and objects. Each learned representation provides a perceptual sensor model for a particular tactile scene. Models trained on actively collected data outperform their randomly collected counterparts in real-time training tests. Additionally, we find that the resulting network entropy maps can be used to identify high salience portions of a tactile scene.

IROS Conference 2024 Conference Paper

Image to Patterning: Density-specified Patterning of Micro-structured Surfaces with a Mobile Robot

Annalisa T. Taylor
Malachi Landis
Yaoke Wang
Todd D. Murphey
Ping Guo

Micro-structured surfaces possess useful properties such as friction modification, anti-fouling, and hydrophobicity. However, manufacturing these surfaces in an affordable, scalable, and efficient manner remains challenging. Standard coverage methods for surface patterning require precise placement of micro-scale features over meter-scale surfaces with expensive tooling for support. In this work, we address the scalability challenge in surface patterning by designing a mobile robot with a credit-card-sized footprint to generate micro-scale divots using a modulated tool tip. We provide a control architecture with a target feature density to specify surface coverage, eliminating the dependence on individual indentation locations. Our robot produces high-fidelity surface patterns and achieves automatic coverage of a surface from sophisticated target images. We validate an exemplary application of such micro-structured surfaces by controlling the friction coefficients at different locations according to the density of indentations. These results show the potential for compact robots to perform scalable manufacturing of functional surfaces, switching the focus from precision machines to small-footprint devices tasked with matching only the density of features.

IROS Conference 2023 Conference Paper

Automated Gait Generation for Walking, Soft Robotic Quadrupeds

Jake Ketchum
Sophia Schiffer
Muchen Sun
Pranav Kaarthik
Ryan L. Truby
Todd D. Murphey

Gait generation for soft robots is challenging due to the nonlinear dynamics and high dimensional input spaces of soft actuators. Limitations in soft robotic control and perception force researchers to hand-craft open loop controllers for gait sequences, which is a non-trivial process. Moreover, short soft actuator lifespans and natural variations in actuator behavior limit machine learning techniques to settings that can be learned on the same time scales as robot deployment. Lastly, simulation is not always possible, due to heterogeneity and nonlinearity in soft robotic materials and their dynamics change due to wear. We present a sample-efficient, simulation free, method for self-generating soft robot gaits, using very minimal computation. This technique is demonstrated on a motorized soft robotic quadruped that walks using four legs constructed from 16 “handed shearing auxetic” (HSA) actuators. To manage the dimension of the search space, gaits are composed of two sequential sets of leg motions selected from 7 possible primitives. Pairs of primitives are executed on one leg at a time; we then select the best-performing pair to execute while moving on to subsequent legs. This method-which uses no simulation, sophisticated computation, or user input-consistently generates good translation and rotation gaits in as low as 4 minutes of hardware experimentation, outperforming hand-crafted gaits. This is the first demonstration of completely autonomous gait generation in a soft robot.

IROS Conference 2023 Conference Paper

Measuring Human-Robot Team Benefits Under Time Pressure in a Virtual Reality Testbed

Katarina Popovic
Millicent Schlafly
Ahalya Prabhakar
Christopher Kim
Todd D. Murphey

During a natural disaster such as hurricane, earthquake, or fire, robots have the potential to explore vast areas and provide valuable aid in search & rescue efforts. These scenarios are often high-pressure and time-critical with dynamically-changing task goals. One limitation to these large scale deployments is effective human-robot interaction. Prior work shows that collaboration between one human and one robot benefits from shared control. Here we evaluate the efficacy of shared control for human-swarm teaming in an immersive virtual reality environment. Although there are many human-swarm interaction paradigms, few are evaluated in high-pressure settings representative of their intended end use. We have developed an open-source virtual reality testbed for realistic evaluation of human-swarm teaming performance under pressure. We conduct a user study ( $\mathrm{n}=16$ ) comparing four human-swarm paradigms to a baseline condition with no robotic assistance. Shared control significantly reduces the number of instructions needed to operate the robots. While shared control leads to marginally improved team performance in experienced participants, novices perform best when the robots are fully autonomous. Our experimental results suggest that in immersive, high-pressure settings, the benefits of robotic assistance may depend on how the human and robots interact, and the human operator's expertise.

ICRA Conference 2021 Conference Paper

Automatic Tuning for Data-driven Model Predictive Control

William Edwards
Gao Tang
Giorgos Mamakoukas
Todd D. Murphey
Kris Hauser

Model predictive control (MPC) is a powerful feedback technique that is often used in data-driven robotics. The performance of data-driven MPC depends on the accuracy of the model, which often requires careful tuning. Furthermore, specifying the task with an objective function and synthesizing a feedback policy are not straightforward and typically lead to suboptimal solutions driven by trial and error. To address these challenges, we present a method to jointly optimize the data-driven system identification, task specification, and control synthesis of unknown dynamical systems. We use our method to develop AutoMPC 3, a software package designed to automate and optimize data-driven MPC. Empirical evaluation on the pendulum swing-up, cart-pole swing-up, and half-cheetah running demonstrates that our method finds data-driven control policies that outperform offline reinforcement learning, without any hand-tuning.

ICRA Conference 2021 Conference Paper

Ergodic imitation: Learning from what to do and what not to do

Aleksandra Kalinowska
Ahalya Prabhakar
Kathleen Fitzsimons
Todd D. Murphey

With growing access to versatile robotics, it is beneficial for end users to be able to teach robots tasks without needing to code a control policy. One possibility is to teach the robot through successful task executions. However, near-optimal demonstrations of a task can be difficult to provide and even successful demonstrations can fail to capture task aspects key to robust skill replication. Here, we propose a learning from demonstration (LfD) approach that enables learning of robust task definitions without the need for near-optimal demonstrations. We present a novel algorithmic framework for learning tasks based on the ergodic metric—a measure of information content in motion. Moreover, we make use of negative demonstrations—demonstrations of what not to do—and show that they can help compensate for imperfect demonstrations, reduce the number of demonstrations needed, and highlight crucial task elements improving robot performance. In a proof-of-concept example of cart-pole inversion, we show that negative demonstrations alone can be sufficient to successfully learn and recreate a skill. Through a human subject study with 24 participants, we show that consistently more information about a task can be captured from combined positive and negative (posneg) demonstrations than from the same amount of just positive demonstrations. Finally, we demonstrate our learning approach on simulated tasks of target reaching and table cleaning with a 7-DoF Franka arm. Our results point towards a future with robust, data-efficient LfD for novice users.

IROS Conference 2021 Conference Paper

Linear Policies are Sufficient to Enable Low-Cost Quadrupedal Robots to Traverse Rough Terrain

Maurice Rahme
Ian Abraham
Matthew L. Elwin
Todd D. Murphey

The availability of inexpensive 3D-printed quadrupedal robots motivates the development of learning-based methods compatible with low-cost embedded processors and position-controlled hobby servos. In this work, we show that a linear policy is sufficient to modulate an open-loop trajectory generator, enabling a quadruped to walk over rough, unknown terrain, with limited sensing. The policy is trained in simulation using randomized terrain and dynamics and directly deployed on the robot. We show that the resulting controller can be implemented on resource-constrained systems. We demonstrate the results by deploying the policy on the OpenQuadruped, an open-source 3D-printed robot equipped with hobby servos and an embedded microprocessor.

IROS Conference 2020 Conference Paper

Bayesian Particles on Cyclic Graphs

Ana Pervan
Todd D. Murphey

We consider the problem of designing synthetic cells to achieve a complex goal (e. g. , mimicking the immune system by seeking invaders) in a complex environment (e. g. , the circulatory system), where they might have to change their control policy, communicate with each other, and deal with stochasticity including false positives and negatives-all with minimal capabilities and only a few bits of memory. We simulate the immune response in cyclic, maze-like environments and use targets at unknown locations to represent invading cells. Using only a few bits of memory, the synthetic cells are programmed to perform a physically-feasible algorithm with which they update their control policy based on randomized encounters with other cells. As the synthetic cells work together to find the target, their interactions as an ensemble function as a physical implementation of a Bayesian update. That is, the particles act as a particle filter. This result provides formal properties about the behavior of the synthetic cell ensemble that can be used to ensure robustness and safety. This method of self-organization is evaluated in simulations, and applied to an actual model of the human circulatory system.

IROS Conference 2020 Conference Paper

Majorization Minimization Methods for Distributed Pose Graph Optimization with Convergence Guarantees

Taosha Fan
Todd D. Murphey

In this paper, we consider the problem of distributed pose graph optimization (PGO) that has extensive applications in multi-robot simultaneous localization and mapping (SLAM). We propose majorization minimization methods for distributed PGO and show that our methods are guaranteed to converge to first-order critical points under mild conditions. Furthermore, since our methods rely a proximal operator of distributed PGO, the convergence rate can be significantly accelerated with Nesterov's method, and more importantly, the acceleration induces no compromise of convergence guarantees. In addition, we also present accelerated majorization minimization methods for the distributed chordal initialization that have a quadratic convergence, which can be used to compute an initial guess for distributed PGO. The efficacy of this work is validated through applications on a number of 2D and 3D SLAM datasets and comparisons with existing state-of-the- art methods, which indicates that our methods have faster convergence and result in better solutions to distributed PGO.

ICRA Conference 2019 Conference Paper

Data-Driven Gait Segmentation for Walking Assistance in a Lower-Limb Assistive Device

Aleksandra Kalinowska
Thomas A. Berrueta
Adam Zoss
Todd D. Murphey

Hybrid systems, such as bipedal walkers, are challenging to control because of discontinuities in their nonlinear dynamics. Little can be predicted about the systems' evolution without modeling the guard conditions that govern transitions between hybrid modes, so even systems with reliable state sensing can be difficult to control. We propose an algorithm that allows for determining the hybrid mode of a system in real-time using data-driven analysis. The algorithm is used with data-driven dynamics identification to enable model predictive control based entirely on data. Two examples-a simulated hopper and experimental data from a bipedal walker-are used. In the context of the first example, we are able to closely approximate the dynamics of a hybrid SLIP model and then successfully use them for control in simulation. In the second example, we demonstrate gait partitioning of human walking data, accurately differentiating between stance and swing, as well as selected subphases of swing. We identify contact events, such as heel strike and toe-off, without a contact sensor using only kinematics data from the knee and hip joints, which could be particularly useful in providing online assistance during walking. Our algorithm does not assume a predefined gait structure or gait phase transitions, lending itself to segmentation of both healthy and pathological gaits. With this flexibility, impairment-specific rehabilitation strategies or assistance could be designed.

IROS Conference 2019 Conference Paper

Efficient and Guaranteed Planar Pose Graph optimization Using the Complex Number Representation

Taosha Fan
Hanlin Wang
Michael Rubenstein
Todd D. Murphey

In this paper, we present CPL-Sync, a certifiably correct algorithm to solve planar pose graph optimization (PGO) using the complex number representation. We formulate planar PGO as the maximum likelihood estimation (MLE) on the product of unit complex numbers, and relax this nonconvex quadratic complex optimization problem to complex semidefinite programming (SDP). Furthermore, we simplify the corresponding semidefinite programming to Riemannian staircase optimization (RSO) on complex oblique manifolds that can be solved with the Riemannian trust region (RTR) method. In addition, we prove that the SDP relaxation and RSO simplification are tight as long as the noise magnitude is below a certain threshold. The efficacy of this work is validated through comparisons with existing methods as well as applications on planar PGO in simultaneous localization and mapping (SLAM), which indicates that the proposed algorithm is capable of solving planar PGO certifiably, and is more efficient in numerical computation and more robust to measurement noises than existing state-of-the-art methods. The C++ code for CPL-Sync is available at https://github.com/fantaosha/CPL-Sync.

ICRA Conference 2015 Conference Paper

Maximizing fisher information using discrete mechanics and projection-based trajectory optimization

Andrew D. Wilson
Todd D. Murphey

This paper reformulates an optimization algorithm previously presented in continuous-time to one using structured integration and structured linearization methods from discrete mechanics. The objective is to synthesize trajectories for dynamic robotic systems that improve the estimation of model parameters by using a metric on Fisher information in a nonlinear projection-based trajectory optimization algorithm. A simulation of a robot with a suspended double pendulum is used as an example system to illustrate the algorithm. Results from the simulation show that the change to a discrete mechanics formulation reduces the computation time by a factor of 19 when compared to the continuous algorithm while maintaining the same two orders of magnitude improvement in the Fisher information from the continuous-time formulation. Through the Cramer-Rao bound, the improvement in the Fisher information results in a maximum expected error reduction of the parameter estimates by up to a factor of 10 2.

ICRA Conference 2015 Conference Paper

Optimal control-on-request: An application in real-time assistive balance control

Anastasia Mavrommati
Alex Ansari
Todd D. Murphey

This paper presents a method for shared control where real-time bursts of optimal control assistance are applied by an observer on-demand to aid a simulated figure in maintaining balance. The proposed Assistive Controller (AC) calculates the optimal burst control fast, in real time, while accounting for nonlinearities of the dynamic model. The short duration of the AC signals allows a rapid transfer of control authority between the nominal and the assistive controller. This scheme avoids prolonged loss of nominal control authority on the part of the figure while facilitating the real-time integration of an external observer's guidance through the assistive control. We demonstrate the benefits of this control scheme in simulation using the Robot Operating System (ROS), in a context where the nominal controller fails to stabilize the figure and the AC is activated intermittently to not only keep it from falling but to additionally push it back to the upright position. The example signifies the efficiency of the proposed model-based AC even in the absence of force/pressure sensors. This approach presents an opportunity for using exoskeletons in balance support, fall prevention, and therapy. In particular, our simulation results indicate that a therapist equipped with an AC interface can, with minimal effort, increase active participation on the part of the patient while ensuring their safety.

IROS Conference 2015 Conference Paper

Real-time trajectory synthesis for information maximization using Sequential Action Control and least-squares estimation

Andrew D. Wilson
Jarvis A. Schultz
Alex Ansari
Todd D. Murphey

This paper presents the details and experimental results from an implementation of real-time trajectory generation and parameter estimation of a dynamic model using the Baxter Research Robot from Rethink Robotics. Trajectory generation is based on the maximization of Fisher information in real-time and closed-loop using a form of Sequential Action Control. On-line estimation is performed with a least-squares estimator employing a nonlinear state observer model computed with trep, a dynamics simulation package. Baxter is tasked with estimating the length of a string connected to a load suspended from the gripper with a load cell providing the single source of feedback to the estimator. Several trials are presented with varying initial estimates showing convergence to the actual length within a 6 second time-frame.

ICRA Conference 2015 Conference Paper

Tactile proprioceptive input in robotic rehabilitation after stroke

Emmanouil Tzorakoleftherakis
Maria C. Bengtson
Ferdinando A. Mussa-Ivaldi
Robert A. Scheidt
Todd D. Murphey

Stroke can lead to loss or impairment of somatosensory sensation (i. e. proprioception), that reduces functional control of limb movements. Here we examine the possibility of providing artificial feedback to make up for lost sensory information following stroke. However, it is not clear whether this kind of sensory substitution is even possible due to stroke-related loss of central processing pathways that subserve somatosensation. In this paper we address this issue in a small cohort of stroke survivors using a tracking task that emulates many activities of daily living. Artificial proprioceptive information was provided to the subjects in the form of vibrotactile cues. The goal was to assist participants in guiding their arm towards a moving target on the screen. Our experiment indicates reliable tracking accuracy under the effect of vibrotactile proprioceptive feedback, even in subjects with impaired natural proprioception. This result is promising and can create new directions in rehabilitation robotics with augmented somatosensory feedback.

IROS Conference 2014 Conference Paper

Improving object tracking through distributed exploration of an information map

Izaak D. Neveln
Lauren M. Miller
Malcolm A. MacIver
Todd D. Murphey

Tracking the position of moving objects requires tight coordination of sensing and movement, in both biological contexts such as prey pursuit and capture, and in target localization by mobile robots. Algorithms for target tracking often use a probabilistic map, or information map, of the domain to guide active search. Though it is reasonable to expect that the best approach would be to choose control actions driving the robot toward the maximum of this information map, we show improved performance in simulation by using a simple heuristic incorporating the time history of robot movement into the map. Furthermore, our results indicate that as the distribution of robot positions approaches the distribution of the density of information, the variance of the estimate is decreased and tracking improves. We conclude that control actions based solely on information maximization may under-perform in information orientated tasks, such as the estimation of moving target positions.

IROS Conference 2013 Conference Paper

Minimal sensitivity control for hybrid environments

Alex Ansari
Todd D. Murphey

This paper presents a method to develop trajectories which remain optimally insensitive to sudden changes in dynamics. The approach is applied to two example systems that model a vehicle's attempt to navigate through potentially hazardous areas of the state space. Through these simplified examples, we show how to automatically plan trajectories which either avoid or adjust controls to safely pass through critical regions of the state space.

IROS Conference 2013 Conference Paper

Optimal planning for information acquisition

Yonatan Silverman
Lauren M. Miller
Malcolm A. MacIver
Todd D. Murphey

This paper presents an algorithm for active search where the goal is to calculate optimal trajectories for autonomous robots during data acquisition tasks. Formulating the problem as parameter estimation enables us to use Fisher information to create an explicit connection between robot dynamics and the informative regions of the search space. We use optimal control to automate design of trajectories that spend time in regions proportional to the probability of collecting informative data and use acquired data to update the probability closed-loop. Experimental and simulated results use a robotic electrosense platform to localize a feature in one-dimension. We demonstrate that this method is robust with respect to disturbances and initial conditions, and results in successful localization of the feature with a 100% experimental success rate and a 34% reduction in localization time compared to the next best tested controller.

ICRA Conference 2012 Conference Paper

Conditions for uniqueness in simultaneous impact with application to mechanical design

Vlad Seghete
Todd D. Murphey

We present a collision resolution method based on momentum maps and show how it extends to handling multiple simultaneous collisions. Simultaneous collisions, which are common in robots that walk or climb, do not necessarily have unique outcomes, but we show that for special configurations-e. g. when the surfaces of contact are orthogonal in the appropriate sense-simultaneous impacts have unique outcomes, making them considerably easier to understand and simulate. This uniqueness helps us develop a measure of the unpredictability of the impact outcome based on the state at impact and is used for gait and mechanism design, such that a mechanism's actions are more predictable and hence controllable. As a preliminary example, we explore the configuration space at impact for a model of the RHex running robot and find optimal configurations at which the unpredictability of the impact outcome is minimized.

IROS Conference 2012 Conference Paper

Simultaneous optimal parameter and mode transition time estimation

Lauren M. Miller
Todd D. Murphey

This paper presents a method of simultaneous mode transition time and parameter estimation for hybrid systems based on switching time optimization techniques. A concise derivation of first- and second-order optimality conditions with respect to both mode transition times and parameter values is presented, including cross-derivative terms between the switching times and the parameters. The estimation algorithm is shown to be effective for estimating transition times as well as unknown parameter values from coarsely sampled data for a skid-steered vehicle, which traverses unknown or changing terrain and transitions between discrete dynamic modes. It is shown that second-order optimization methods using the exact Hessian provide far superior convergence, compared to first-or approximate second-order methods, to correct values in simulated and experimental scenarios.

ICRA Conference 2012 Conference Paper

Trajectory generation for underactuated control of a suspended mass

Jarvis A. Schultz
Todd D. Murphey

The underactuated system under consideration is a magnetically-suspended, differential drive robot utilizing a winch system to articulate a suspended mass. A dynamic model of the system is first constructed, and then a nonlinear, infinite-dimensional optimization algorithm is presented. The system model uses the principles of kinematic reduction to produce a mixed kinematic-dynamic model that isolates the modeling of the system actuators from the modeling of the rest of the system. In this framework, the inputs become generalized velocities instead of generalized forces facilitating real-world implementation with an embedded system. The optimization algorithm automatically deals with the complexities introduced by the nonlinear dynamics and underactuation to synthesize dynamically feasible system trajectories for a wide array of trajectory generation problems. Applying this algorithm to the mixed kinematic-dynamic model, several example problems are solved and the results are tested experimentally. The experimental results agree quite well with the theoretical showing promise in extending the capabilities of the system to utilize more advanced feedback techniques and to handle more complex, three-dimensional problems.

ICRA Conference 2012 Conference Paper

Trajectory tracking among landmarks and binary sensor-beams

Benjamín Tovar
Todd D. Murphey

We study a trajectory tracking problem for a mobile robot moving in the plane using combinatorial observations of the state. These observations come from crossing binary detection beams. A binary detection beam is a sensing abstraction arising from physical sensor beams or virtual beams that are derived from several sensing modalities, such as actual detection beams in the environment, changes in the angular order of landmarks around the robot, or recognizable markings in the plane. We solve the filtering problem from a geometric perspective and present its relation to linear recursive filters in control theory. Subsequently, we develop the acceleration control of the robot to track a given input trajectory, with a finite control set consisting on moving toward landmarks naturally modeling the robot as a switched dynamical system. We present experiments using an e-puck differential-drive robot, in which a useful estimate of the state for tracking is produced regardless of nontrivial uncertainty.

ICRA Conference 2011 Conference Paper

Optimal motion planning for a class of hybrid dynamical systems with impacts

Andrew W. Long
Todd D. Murphey
Kevin M. Lynch

Hybrid dynamical systems with impacts typically have controls that can influence the time of the impact as well as the result of the impact. The leg angle of a hopping robot is an example of an impact control because it can influence when the impact occurs and the direction of the impulse. This paper provides a method for computing an explicit expression for the first derivative of a cost function encoding a desired trajectory. The first derivative can be used with standard optimization algorithms to find the optimal impact controls for motion planning of hybrid dynamical systems with impacts. The resulting derivation is implemented for a simplified model of a dynamic climbing robot.

ICRA Conference 2010 Conference Paper

Relaxed optimization for mode estimation in skid steering

Timothy M. Caldwell
Todd D. Murphey

Skid-steered vehicles, by design, must skid in order to maneuver. The skidding causes the vehicle to behave discontinuously as well as introduces complications to the observation of the vehicle's state, both of which affect a controller's performance. This paper addresses estimation of contact state by applying switched system optimization to estimate skidding properties of the skid-steered vehicle. In order to treat the skid-steered vehicle as a switched system, the vehicle's ground interaction is modeled using Coulomb friction, thereby partitioning the system dynamics into four distinct modes, one for each combination of the forward and back wheel pairs sticking or skidding. Thus, as the vehicle maneuvers, the system propagates over some mode sequence, transitioning between modes over some set of switching times. This paper presents a technique for estimating a mode sequence by optimizing a relaxation of an infinite dimensional representation of switched systems. The switching times themselves may then be estimated using switching time optimization techniques.

ICRA Conference 2010 Conference Paper

Variational solutions to simultaneous collisions between multiple rigid bodies

Vlad Seghete
Todd D. Murphey

We present a method of resolving simultaneous collisions between multiple rigid bodies based on the least action principle. By using the generalized directional derivative of the action, we use that the solution is related to the outcomes of nearby trajectories that experience consecutive single impacts. We present an algorithm based on this result, and prove its effectiveness by applying it to several low dimensionality examples based on billiard ball interactions, including a simplified version of Newton's cradle.

ICRA Conference 2008 Conference Paper

Adaptive cooperative manipulation with intermittent contact

Todd D. Murphey
Matanya B. Horowitz

Cooperative manipulation with multiple, independent agents can be complicated by changing dynamics as the agents come in and out of contact with the object they are manipulating. This effect, combined with uncertainty in the environment, leads to nontrivial issues in terms of guaranteeing convergence and task completion. Here we illustrate how these effects can be mitigated using a decentralized adaptive control technique based on hybrid control. Results are verified in an experiment using three agents.

ICRA Conference 2008 Conference Paper

Discrete and continuous mechanics for tree representations of mechanical systems

Elliot R. Johnson
Todd D. Murphey

We use a tree-based structure to represent mechanical systems comprising interconnected rigid bodies. Using this representation, we derive a simple algorithm to numerically calculate forward kinematic maps, body velocities, and their derivatives. The algorithm is computationally efficient and scales to large systems very well by using recursion to take advantage of the tree structure. Moreover, this method is less prone to modeling errors because each element of the graph is simple. The tree representation provides a natural framework to simulate mechanical dynamics with numeric computations rather than large symbolically-derived equations. In particular, the representation allows one to simulate systems in generalized coordinates using Lagrangian dynamics without symbolically finding the equations of motion. This method also applies to the relatively new variational integrators which numerically integrate dynamics in a way that preserve momentum and other symmetries. We show how to implement both integration schemes for an arbitrary system of interconnected rigid bodies in a computationally efficient way while avoiding symbolic equations of motion. We end with an example simulating a marionette; a mechanically complex, high degree-of-freedom system.

ICRA Conference 2007 Conference Paper

Dynamic Modeling and Motion Planning for Marionettes: Rigid Bodies Articulated by Massless Strings

Elliot R. Johnson
Todd D. Murphey

We consider the problem of modeling a robotic marionette. Marionettes are highly under-actuated systems that can only be controlled remotely by moving strings. We present a mixed dynamic-kinematic modeling technique that removes the controller dynamics from the marionette, resulting in a clean abstraction that represents the dynamics of the marionette in a natural way. As an example, a model is derived for a single arm moving in a plane. A model for a three-dimensional marionettes is also shown. Finally, an expansive-space tree (EST) motion planner is used to find a path from an input configuration to a goal for a puppet arm with seven degrees of freedom.

ICRA Conference 2006 Conference Paper

A Method of Cooperative Control using Occasional non-local Interactions

Brian Shucker
Todd D. Murphey
John K. Bennett

Current approaches to distributed control involving many robots generally restrict interactions to pairs of robots within a threshold distance. While this allows for provable stability, there are performance costs associated with the lack of long-distance information. We introduce the acute angle switching algorithm, which allows a small number of long-range interactions in addition to interactions with nearby neighbors, without sacrificing provable stability. We prove several formal properties of the acute angle switching algorithm, including system-wide connectivity. Further, we show simulation results demonstrating the efficacy and robustness of multi-robot systems based on the acute angle switching algorithm

ICRA Conference 2006 Conference Paper

Motion Planning for Kinematically Overconstrained Vehicles using Feedback Primitives

Todd D. Murphey

In this paper we consider motion planning for kinematically overconstrained vehicles. Such vehicles are reasonably common in applications that require many axles for static stability. When a system is kinematically overconstrained, typically some contacts with the environment must slip, violating the constraint. This introduces nonsmooth behavior into the equations of motion, making classical motion planning strategies inapplicable. As an example, we consider a vehicle that has a simplified version of the kinematic structure of the rover from the first Mars mission. We introduce a provably complete motion planner for purposes of illustration. However, the primary purpose of this paper is to clearly identify some of the open problems in motion planning for these mechanisms and to propose a kinematic modeling framework that reveals the underlying complications due to slipping while maintaining the relative simplicity associated with kinematic systems over dynamic ones. The planner we describe has properties that we anticipate would be relevant to a general methodology for motion planning for both kinematically overconstrained systems as well as more general systems that have uncertain dynamics

IROS Conference 2005 Conference Paper

An example of parts handling and self-assembly using stable limit sets

Todd D. Murphey
Jay Bernheisel
David Choi
Kevin M. Lynch

Throwing and catching parts, similar to vibratory agitation, promises to be a powerful manipulation technique, but is analytically complicated by equations of motion involving friction and impacts. However, one can show that some simple part manipulators exhibit limit set behavior, where the parts enter a set that is invariant under the mapping that corresponds to the throwing action. We show that by analyzing limit sets directly we can design parts and their environment so that part feeding or assembling naturally emerges from the dynamics. We include experiments validating both these approaches and a discussion of future work.

ICRA Conference 2003 Conference Paper

Experiments in nonsmooth control of distributed manipulation

Todd D. Murphey
Joel W. Burdick
James Burgess
Andrew Homyk

This paper describes an experimental modular distributed manipulation system upon which one can implement a variety of control schemes. We have shown elsewhere that when one includes the nonsmooth effects of friction into a model of distributed manipulation, nonsmooth feedback laws must generally be used to control distributed manipulators. We summarize results obtained with this experimental system that confirm the validity of control schemes proposed by the authors in recent papers. We describe the control algorithms in some detail and include specifics of the experimental set-up and experimental results.

ICRA Conference 2003 Conference Paper

Smooth feedback control algorithms for distributed manipulators

Todd D. Murphey
Joel W. Burdick

This paper introduces a smooth control algorithm for controlling fully actuated distributed manipulation systems that operate by frictional contact. The control law scales linearly with the number of actuators and is simple to implement. Moreover, we prove that control law has desirable robustness properties in the presence of the nonsmooth mechanics inherent in distributed manipulation systems that rely upon frictional contact. This algorithm has been implemented on an experimental distributed manipulation test-bed, whose structure is briefly reviewed. The experimental results confirm the validity and performance of the algorithm.

ICRA Conference 2002 Conference Paper

Global Exponential Stabilizability for Distributed Manipulation Systems

Todd D. Murphey
Joel W. Burdick

Considers the global exponential stability of planar distributed manipulation control schemes. The programmable vector field approach is a commonly proposed method for distributed manipulation control. The authors (2001) showed that when one takes into account the discreteness of actuator arrays and the mechanics of actuator/object contact, the controls designed by the programmable vector field approach can be unstable at the desired equilibrium configuration. We show here how a discontinuous feedback law that locally stabilizes the manipulated object at the equilibrium can be combined with the programmable vector field approach to control the object's motions. We prove that the combined system is globally exponentially stabilizable even in the presence of changes in contact state. Simulations illustrate the results.

ICRA Conference 2001 Conference Paper

A Controllability test and Motion planning Primitives for Overconstrained Vehicles

Todd D. Murphey
Joel W. Burdick

Conventional nonholonomic motion planning and control theories do not directly apply to "overconstrained vehicles", such as the Sojourner vehicle of the Mars Pathfinder mission. This paper discusses some basic issues of motion planning and control for this potentially important class of mobile robots. A power dissipation approach is used to model the governing equations of overconstrained vehicles that move quasi-statically. These equations are shown to be switched hybrid systems. Notions from standard geometric control, such as the Lie bracket, are extended to these switched systems. We then develop a controllability test for such systems. We explore motion planning primitives in the context of simplified examples.

IROS Conference 2001 Conference Paper

Global stability for distributed systems with changing contact states

Todd D. Murphey
Joel W. Burdick

Analyzes the global stability of distributed manipulation control schemes. The "programmable vector field" approach, which assumes that the system's control actions can be approximated by a continuous vector force field, is a commonly proposed scheme for distributed manipulation control. In practical implementations, the continuous control force field idealization must then be adapted to the specifics of the discrete physical actuator array. However, in Murphey and Burdick (2001) it was shown that when one takes into account the discreteness of actuator arrays and realistic models of the actuator/object contact mechanics, the controls designed by the continuous approximation approach can be unstable at the desired equilibrium configuration. We introduced a discontinuous feedback law that locally stabilizes the manipulated object at the equilibrium. However, the stability of this feedback law only holds in a neighborhood of the equilibrium. In this paper we show how to combine the programmable vector field approach and our local feedback stabilization law to achieve a globally stable distributed manipulation control system. Simulations illustrate the method.

ICRA Conference 2001 Conference Paper

On the Stability and Design of Distributed Manipulation Control Systems

Todd D. Murphey
Joel W. Burdick

Analyzes the stability of distributed manipulation control schemes. A commonly proposed method for designing a distributed actuator array control scheme assumes that the system's control action can be approximated by a continuous vector force field. The continuous control vector field idealization must then be adapted to the physical actuator array. However, we show that when one takes into account the discreteness of actuator arrays and realistic models of the actuator/object contact mechanics, the controls designed by the continuous approximation approach can be unstable. For this analysis we introduce and use a "power dissipation" method that captures the contact mechanics in a general but tractable way. We show that the quasi-static contact equations have the form of a switched hybrid system. We introduce a discontinuous feedback law that can produce stability which is robust with respect to variations in contact state.