Koopman operator theory offers a rigorous treatment of dynamics, emerging as a robust alternative for learning-based control in robotics. By representing nonlinear dynamics as a linear, higher-dimensional operator, it provides a fresh lens for modeling complex systems. Its ability to support incremental updates and low computational cost makes it particularly appealing for real-time applications and online learning. This review delves deeply into the foundations, systematically bridging theoretical principles to practical robotic applications. We explain mathematical underpinnings, approximation approaches for inputs, data collection strategies, and lifting function design. We explore how Koopman models unify tasks like model-based control, state estimation, and motion planning. The review surveys cutting-edge research across domains ranging from aerial and legged platforms to manipulators, soft robots, and multi-agent networks. We also present advanced theoretical topics and reflect on open challenges and future research directions. To support adoption, we provide a hands-on tutorial with code athttps://github.com/sunnyshi0310/KoopmanRobo/tree/main.

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

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.

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.

Ergodic search enables optimal exploration of an information distribution with guaranteed asymptotic coverage of the search space. However, current methods typically have exponential computational complexity and are limited to Euclidean space. We introduce a computationally efficient ergodic search method. Our contributions are two-fold as follows: First, we develop a kernel-based ergodic metric, generalizing it from Euclidean space to Lie groups. We prove this metric is consistent with the exact ergodic metric and ensures linear complexity. Second, we derive an iterative optimal control algorithm for trajectory optimization with the kernel metric. Numerical benchmarks show our method is two orders of magnitude faster than the state-of-the-art method. Finally, we demonstrate the proposed algorithm with a peg-in-hole insertion task. We formulate the problem as a coverage task in the space of SE(3) and use a 30-s-long human demonstration as the prior distribution for ergodic coverage. Ergodicity guarantees the asymptotic solution of the peg-in-hole problem so long as the solution resides within the prior information distribution, which is seen in the 100% success rate.

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.

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.

We consider the problem of distributed pose graph optimization (PGO) that has important applications in multirobot simultaneous localization and mapping (SLAM). We propose the majorization minimization (MM) method for distributed PGO ($\mathsf {MM\text{--}PGO}$) that applies to a broad class of robust loss kernels. The$\mathsf {MM\text{--}PGO}$method is guaranteed to converge to first-order critical points under mild conditions. Furthermore, noting that the$\mathsf {MM\text{--}PGO}$method is reminiscent of proximal methods, we leverage Nesterov's method and adopt adaptive restarts to accelerate convergence. The resulting accelerated MM methods for distributed PGO—both with a master node in the network ($\mathsf {AMM\text{--}PGO}^*$) and without ($\mathsf {AMM\text{--}PGO}^{\#}$)—have faster convergence in contrast to the$\mathsf {MM\text{--}PGO}$method without sacrificing theoretical guarantees. In particular, the$\mathsf {AMM\text{--}PGO}^{\#}$method, which needs no master node and is fully decentralized, features a novel adaptive restart scheme and has a rate of convergence comparable to that of the$\mathsf {AMM\text{--}PGO}^*$method using a master node to aggregate information from all the nodes. The efficacy of this work is validated through extensive applications to 2-D and 3-D SLAM benchmark datasets and comprehensive comparisons against existing state-of-the-art methods, indicating that our MM methods converge faster and result in better solutions to distributed PGO.

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.

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.

In this article, we develop the method of continuous Pontryagin differentiable programming (Continuous PDP), which enables a robot to learn an objective function from a few sparsely demonstrated keyframes. The keyframes, labeled with some time stamps, are the desired task-space outputs, which a robot is expected to follow sequentially. The time stamps of the keyframes can be different from the time of the robot's actual execution. The method jointly finds an objective function and a time-warping function such that the robot's resulting trajectory sequentially follows the keyframes with minimal discrepancy loss. The Continuous PDP minimizes the discrepancy loss using projected gradient descent by efficiently solving the gradient of the robot trajectory with respect to the unknown parameters. The method is first evaluated on a simulated robot arm and then applied to a 6-DoF quadrotor to learn an objective function for motion planning in unmodeled environments. The results show the efficiency of the method, its ability to handle time misalignment between keyframes and robot execution, and the generalization of objective learning into unseen motion conditions.

This article proposes a novel approach that enables a robot to learn an objective function incrementally from human directional corrections. Existing methods learn from human magnitude corrections; since a human needs to carefully choose the magnitude of each correction, those methods can easily lead to overcorrections and learning inefficiency. The proposed method only requires human directional corrections—corrections that only indicate the direction of an input change without indicating its magnitude. We only assume that each correction, regardless of its magnitude, points in a direction that improves the robot's current motion relative to an unknown objective function. The allowable corrections satisfying this assumption account for half of the input space, as opposed to the magnitude corrections that have to lie in a shrinking level set. For each directional correction, the proposed method updates the estimate of the objective function based on a cutting plane method, which has a geometric interpretation. We have established theoretical results to show the convergence of the learning process. The proposed method has been tested in numerical examples, a user study on two human–robot games, and a real-world quadrotor experiment. The results confirm the convergence of the proposed method and further show that the method is significantly more effective (higher success rate), efficient/effortless (less human corrections needed), and potentially more accessible (fewer early wasted trials) than the state-of-the-art robot learning frameworks.

In this article, we demonstrate the benefits of imposing stability on data-driven Koopman operators. The data-driven identification of stable Koopman operators (DISKO) is implemented using an algorithm [1] that computes the neareststablematrix solution to a least-squares reconstruction error. As a first result, we derive a formula that describes the prediction error of Koopman representations for an arbitrary number of time steps, and which shows that stability constraints can improve the predictive accuracy over long horizons. As a second result, we determine formal conditions on basis functions of Koopman operators needed to satisfy the stability properties of an underlying nonlinear system. As a third result, we derive formal conditions for constructing Lyapunov functions for nonlinear systems out of stable data-driven Koopman operators, which we use to verify stabilizing control from data. Finally, we demonstrate the benefits of DISKO in prediction and control with simulations using a pendulum and a quadrotor and experiments with a pusher-slider system. The paper is complemented with a video:https://sites.google.com/view/learning-stable-koopman.

Advances in exoskeletons and robot arms have given us increasing opportunities for providing physical support and meaningful feedback in training and rehabilitation settings. However, the chosen control strategies must support motor learning and provide mathematical task definitions that are actionable for the actuation. Typical robot control architectures rely on measuring error from a reference trajectory. In physical human-robot interaction, this leads to low engagement, invariant practice, and few errors, which are not conducive to motor learning. A reliance on reference trajectories means that the task definition is both over-specified—requiring specific timings not critical to task success—and lacking information about normal variability. In this article, we examine a way to define tasks and close the loop using an ergodic measure that quantifies how much information about a task is encoded in the human-robot motion. This measure can capture the natural variability that exists in typical human motion, enabling therapy based on scientific principles of motor learning. We implement an ergodic hybrid shared controller (HSC) on a robotic arm as well as an error-based controller—virtual fixtures—in a timed drawing task. In a study of 24 participants, we compare ergodic HSC with virtual fixtures and find that ergodic HSC leads to improved training outcomes.

We propose a novel sparse constrained formulation and from it derive a real-time optimization method for 3D human pose and shape estimation. Our optimization method, SCOPE (Sparse Constrained Optimization for 3D human Pose and shapE estimation), is orders of magnitude faster (avg. 4ms convergence) than existing optimization methods, while being mathematically equivalent to their dense unconstrained formulation under mild assumptions. We achieve this by exploiting the underlying sparsity and constraints of our formulation to efficiently compute the Gauss-Newton direction. We show that this computation scales linearly with the number of joints and measurements of a complex 3D human model, in contrast to prior work where it scales cubically due to their dense unconstrained formulation. Based on our optimization method, we present a real-time motion capture framework that estimates 3D human poses and shapes from a single image at over 30 FPS. In benchmarks against state-of-the-art methods on multiple public datasets, our framework outperforms other optimization methods and achieves competitive accuracy against regression methods. Project page with code and videos: https://sites.google.com/view/scope-human/.

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 AutoMPC3, 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.

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.

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.

This article develops KL-ergodic exploration from equilibrium (KL-E3), a method for robotic systems to integrate stability into actively generating informative measurements through ergodic exploration. Ergodic exploration enables robotic systems to indirectly sample from informative spatial distributions globally, avoiding local optima, and without the need to evaluate the derivatives of the distribution against the robot dynamics. Using a hybrid systems theory, we derive a controller that allows a robot to exploit equilibrium policies (i.e., policies that solve a task) while allowing the robot to explore and generate informative data using an ergodic measure that can extend to high-dimensional states. We show that our method is able to maintain Lyapunov attractiveness with respect to the equilibrium task while actively generating data for learning tasks such, as Bayesian optimization, model learning, and off-policy reinforcement learning. In each example, we show that our proposed method is capable of generating an informative distribution of data while synthesizing smooth control signals. We illustrate these examples using simulated systems and provide simplification of our method for real-time online learning in robotic systems.Note to Practitioners—Robotic systems need to adapt to sensor measurements and learn to exploit an understanding of the world around them such that they can truly begin to experiment in the real world. Standard learning methods do not have any restrictions on how the robot can explore and learn, making the robot dynamically volatile. Those that do are often too restrictive in terms of the stability of the robot, resulting in a lack of improved learning due to poor data collection. Applying our method would allow robotic systems to be able to adapt online without the need for human intervention. We show that considering both the dynamics of the robot and the statistics of where the robot has been, we are able to naturally encode where the robot needs to explore and collect measurements for efficient learning that is dynamically safe. With our method, we are able to effectively learn while being energetically efficient compared with state-of-the-art active learning methods. Our approach accomplishes such tasks in a single execution of the robotic system, i.e., the robot does not need human intervention to reset it. Future work will consider multiagent robotic systems that actively learn and explore in a team of collaborative robots.

In nature, biological organisms jointly evolve both their morphology and their neurological capabilities to improve their chances for survival. Consequently, task information is encoded in both their brains and their bodies. In robotics, the development of complex control and planning algorithms often bears sole responsibility for improving task performance. This dependence on centralized control can be problematic for systems with computational limitations, such as mechanical systems and robots on the microscale. In these cases, we need to be able to offload complex computation onto the physical morphology of the system. To this end, we introduce a methodology for algorithmically arranging sensing and actuation components into a robot design while maintaining a low level of design complexity (quantified using a measure of graph entropy) and a high level of task embodiment (evaluated by analyzing the Kullback–Leibler divergence between physical executions of the robot and those of an idealized system). This approach computes an idealized, unconstrained control policy that is projected onto a limited selection of sensors and actuators in a given library, resulting in intelligence that is distributed away from a central processor and instead embodied in the physical body of a robot. The method is demonstrated by computationally optimizing a simulated synthetic cell.Note to Practitioners—As robotic systems approach the micrometer scale, designing them to be fully autonomous will rely less on onboard computation and more on component selection and design. In this article, we are motivated by synthetic cells—microscopic devices with limited actuation, sensing, and memory components. We apply tools from optimal control, graph theory, and information theory to develop a methodology for designing the electronic circuitry that relates actuation to sensing using memory and physically realizable transformations (e.g., simple logical operators). Results indicate that encoding task information in the physical body of a robot via a simple control policy leads to successful task performance. In future work, we plan to apply these methods to different robotic systems and to experimentally employ these designs on actual synthetic cells.

This article presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using higher order derivatives of general nonlinear dynamics that need not be known, we construct a Koopman-operator-based linear representation and utilize Taylor series accuracy analysis to derive an error bound. The resulting error formula is used to choose the order of derivatives in the basis functions and obtain a data-driven Koopman model using a closed-form expression that can be computed in real time. Using the inverted pendulum system, we illustrate the robustness of the error bounds given noisy measurements of unknown dynamics, where the derivatives are estimated numerically. When combined with control, the Koopman representation of the nonlinear system has marginally better performance than competing nonlinear modeling methods, such as SINDy and NARX. In addition, as a linear model, the Koopman approach lends itself readily to efficient control design tools, such as linear–quadratic regulator, whereas the other modeling approaches require nonlinear control methods. The efficacy of the approach is further demonstrated with simulation and experimental results on the control of a tail-actuated robotic fish. Experimental results show that the proposed data-driven control approach outperforms a tuned proportional–integral–derivative controller and that updating the data-driven model online significantly improves performance in the presence of unmodeled fluid disturbance. This article is complemented with a video available athttps://youtu.be/9_wx0tdDta0.

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.

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.

Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a recent characterization of stable matrices, we present an optimization method that ensures stability at every step and iteratively improves the reconstruction error using gradient directions derived in this paper. When applied to LDSs with inputs, our approach---in contrast to current methods for learning stable LDSs---updates both the state and control matrices, expanding the solution space and allowing for models with lower reconstruction error. We apply our algorithm in simulations and experiments to a variety of problems, including learning dynamic textures from image sequences and controlling a robotic manipulator. Compared to existing approaches, our proposed method achieves an \textit{orders-of-magnitude} improvement in reconstruction error and superior results in terms of control performance. In addition, it is \textit{provably} more memory efficient, with an $\mathcal{O}(n^2)$ space complexity compared to $\mathcal{O}(n^4)$ of competing alternatives, thus scaling to higher-dimensional systems when the other methods fail. The code of the proposed algorithm and animations of the results can be found at https://github.com/giorgosmamakoukas/MemoryEfficientStableLDS.

In this article, we consider the problem of planar graph-based simultaneous localization and mapping (SLAM) that involves both poses of the autonomous agent and positions of observed landmarks. We present complex (CPL)-SLAM, an efficient and certifiably correct algorithm to solve planar graph-based SLAM using the complex number representation. We formulate and simplify planar graph-based SLAM as the maximum likelihood estimation on the product of unit complex numbers, and relax this nonconvex quadratic complex optimization problem to convex complex semidefinite programming (SDP). Furthermore, we simplify the corresponding complex SDP to Riemannian staircase optimization (RSO) on the complex oblique manifold that can be solved with the Riemannian trust region 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 applications of CPL-SLAM and comparisons with existing state-of-the-art methods on planar graph-based SLAM, which indicates that our proposed algorithm is capable of solving planar graph-based SLAM certifiably, and is more efficient in numerical computation and more robust to measurement noise than existing state-of-the-art methods. The C++ code for CPL-SLAM is available at https://github.com/MurpheyLab/CPL-SLAM.

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.

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.

This paper presents an active learning strategy for robotic systems that takes into account task information, enables fast learning, and allows control to be readily synthesized by taking advantage of the Koopman operator representation. We first motivate the use of representing nonlinear systems as linear Koopman operator systems by illustrating the improved model-based control performance with an actuated Van der Pol system. Information-theoretic methods are then applied to the Koopman operator formulation of dynamical systems where we derive a controller for active learning of robot dynamics. The active learning controller is shown to increase the rate of information about the Koopman operator. In addition, our active learning controller can readily incorporate policies built on the Koopman dynamics, enabling the benefits of fast active learning and improved control. Results using a quadcopter illustrate single-execution active learning and stabilization capabilities during free fall. The results for active learning are extended for automating Koopman observables and we implement our method on real robotic systems.

Although a number of solutions exist for the problems of coverage, search, and target localization-commonly addressed separately-whether there exists a unified strategy that addresses these objectives in a coherent manner without being application specific remains a largely open research question. In this paper, we develop a receding-horizon ergodic control approach, based on hybrid systems theory, that has the potential to fill this gap. The nonlinear model-predictive control algorithm plans real-time motions that optimally improve ergodicity with respect to a distribution defined by the expected information density across the sensing domain. We establish a theoretical framework for global stability guarantees with respect to a distribution. Moreover, the approach is distributable across multiple agents so that each agent can independently compute its own control while sharing statistics of its coverage across a communication network. We demonstrate the method in both simulation and in experiment in the context of target localization, illustrating that the algorithm is independent of the number of targets being tracked and can be run in real time on computationally limited hardware platforms.

This paper presents experimental results from the real-time parameter estimation of a system model and subsequent trajectory optimization for a dynamic task using the Baxter Research Robot from Rethink Robotics. An active estimator maximizing Fisher information is used in real time with a closed-loop, nonlinear control technique known as sequential action control. 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. Following the active estimation, a trajectory is generated using the trep software package that controls Baxter to dynamically swing a suspended load into a box. Several trials are presented with varying initial estimates showing that the estimation is required to obtain adequate open-loop trajectories to complete the prescribed task. The result of one trial with and without the active estimation is also shown in the accompanying video.

The laws of physics establish the energetic efficiency of our movements. In some cases, like locomotion, the mechanics of the body dominate in determining the energetically optimal course of action. In other tasks, such as manipulation, energetic costs depend critically upon the variable properties of objects in the environment. Can the brain identify and follow energy-optimal motions when these motions require moving along unfamiliar trajectories? What feedback information is required for such optimal behavior to occur? To answer these questions, we asked participants to move their dominant hand between different positions while holding a virtual mechanical system with complex dynamics (a planar double pendulum). In this task, trajectories of minimum kinetic energy were along curvilinear paths. Our findings demonstrate that participants were capable of finding the energy-optimal paths, but only when provided with veridical visual and haptic information pertaining to the object, lacking which the trajectories were executed along rectilinear paths.

This paper introduces and implements a method for real-time mode scheduling in linear time-varying switched systems subject to a quadratic cost functional. The execution time of switched system algorithms is often prohibitive for real-time applications and typically may only be reduced at the expense of approximation accuracy. We address this tradeoff by taking advantage of system linearity to formulate a projection-based approach, such that no simulation is required during open-loop optimization. A numerical example shows how the proposed open-loop algorithm outperforms the methods employing common numerical integration techniques. In addition, we follow a receding-horizon scheme to schedule the modes of a customized experimental setup in real time, using the robot operating system. In particular, we demonstrate-both in Monte Carlo simulation and in experiment-that optimal mode scheduling efficiently regulates a cart and suspended mass system and rejects disturbances online.

This paper presents a new model-based algorithm that computes predictive optimal controls online and in a closed loop for traditionally challenging nonlinear systems. Examples demonstrate the same algorithm controlling hybrid impulsive, underactuated, and constrained systems using only high-level models and trajectory goals. Rather than iteratively optimizing finite horizon control sequences to minimize an objective, this paper derives a closed-form expression for individual control actions, i.e., control values that can be applied for short duration, that optimally improve a tracking objective over a long time horizon. Under mild assumptions, actions become linear feedback laws near equilibria that permit stability analysis and performance-based parameter selection. Globally, optimal actions are guaranteed existence and uniqueness. By sequencing these actions online, in receding horizon fashion, the proposed controller provides a min-max constrained response to a state that avoids the overhead typically required to impose control constraints. Benchmark examples show that the approach can avoid local minima and outperform nonlinear optimal controllers and recent case-specific methods in terms of tracking performance and at speeds that are orders of magnitude faster than traditionally achievable ones.

This paper presents an active search trajectory synthesis technique for autonomous mobile robots with nonlinear measurements and dynamics. The presented approach uses the ergodicity of a planned trajectory with respect to an expected information density map to close the loop during search. The ergodic control algorithm does not rely on discretization of the search or action spaces and is well posed for coverage with respect to the expected information density whether the information is diffuse or localized, thus trading off between exploration and exploitation in a single-objective function. As a demonstration, we use a robotic electrolocation platform to estimate location and size parameters describing static targets in an underwater environment. Our results demonstrate that the ergodic exploration of distributed information algorithm outperforms commonly used information-oriented controllers, particularly when distractions are present.

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.

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.

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 102.

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.

Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they are not energy-preserving they do exhibit long-time stable energy behavior. However, variational integrators often simulate mechanical system dynamics by solving an implicit difference equation at each time step, one that is moreover expressed purely in terms of configurations at different time steps. This paper formulates the first- and second-order linearizations of a variational integrator in a manner that is amenable to control analysis and synthesis, creating a bridge between existing analysis and optimal control tools for discrete dynamic systems and variational integrators for mechanical systems in generalized coordinates with forcing and holonomic constraints. The forced pendulum is used to illustrate the technique. A second example solves the discrete Linear Quadratic Regulator (LQR) problem to find a locally stabilizing controller for a 40 DOF system with six constraints.

When attempting to estimate parameters in a dynamical system, it is often beneficial to strategically design experimental trajectories that facilitate the estimation process. This paper presents an optimization algorithm which improves conditioning of estimation problems by modifying the experimental trajectory. An objective function which minimizes the condition number of the Hessian of the least-squares identification method is derived and a least-squares method is used to estimate parameters of the nonlinear system. A software-simulated example demonstrates that an arbitrarily designed trajectory can lead to an ill-conditioned least-squares estimation problem, which in turn leads to slower convergence to the best estimate and, in the presence of experimental uncertainties, may lead to no convergence at all. A physical experiment with a robot-controlled suspended mass also shows improved estimation results in practice in the presence of noise and uncertainty using the optimized trajectory.

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.

This paper presents existence and uniqueness results for a propagative model of simultaneous impacts that is guaranteed to conserve energy and momentum in the case of elastic impacts with extensions to perfectly plastic and inelastic impacts. A corresponding time-stepping algorithm that guarantees conservation of continuous energy and discrete momentum is developed, also with extensions to plastic and inelastic impacts. The model is illustrated in simulation using billiard balls and a two-dimensional legged robot as examples; the latter is optimized over geometry and gait parameters to achieve unique simultaneous impacts.

Estimation of model parameters in a dynamic system can be significantly improved with the choice of experimental trajectory. For general nonlinear dynamic systems, finding globally "best" trajectories is typically not feasible; however, given an initial estimate of the model parameters and an initial trajectory, we present a continuous-time optimization method that produces a locally optimal trajectory for parameter estimation in the presence of measurement noise. The optimization algorithm is formulated to find system trajectories that improve a norm on the Fisher information matrix (FIM). A double-pendulum cart apparatus is used to numerically and experimentally validate this technique. In simulation, the optimized trajectory increases the minimum eigenvalue of the FIM by three orders of magnitude, compared with the initial trajectory. Experimental results show that this optimized trajectory translates to an order-of-magnitude improvement in the parameter estimate error in practice.

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.

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.

This paper focuses on detecting and localizing a surface feature on an otherwise uniform surface using kinematic data collected during an exploratory procedure. Assuming that characteristics of the feature shape and surface shape are known, a surface feature is detected by performing least squares estimation calculated via impulsive hybrid system optimization. The optimization routine is based on an adjoint formulation which allows the algorithm to be computationally efficient and scalable. This algorithm is also shown to perform well with the presence of measurement noise and model noise, both in simulations and experiments.

An optimization-based estimation method is presented to determine mode transition times and model parameters for hybrid systems. First- and second-order optimality conditions are derived, including cross-derivative terms between transition times and parameters. Second-order optimization methods are shown to provide superior convergence to correct values in simulation, and to values within expected ranges experimentally for traction estimation of a skid-steered vehicle.

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.

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.

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.

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.

First- and second-order solution methods for the multi-target data association problem with an unknown number of targets are presented. It is shown that by considering a single continuous measurement signal with impulsive switching between measuring the position of different objects, the data association problem can be recast as a continuous optimization over the impulse times and magnitudes. First- and second-order adjoint formulations are derived which reduce the calculation of the either the first- or second-order derivative of the cost function to a single integration (over any number of impulse times and magnitudes). These adjoint formulations as well as a method for estimating the total number of impulses which occur are the main contributions of this work.

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.

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.

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.

We present a technique to implement scalable variational integrators for generic mechanical systems in generalized coordinates. Systems are represented by a tree-based structure that provides efficient means to algorithmically calculate values (position, velocities, and derivatives) needed for variational integration without the need to resort to explicit equations of motion. The variational integrator handles closed kinematic chains, holonomic constraints, dissipation, and external forcing without modification. To avoid the full equations of motion, this method uses recursive equations, and caches calculated values, to scale to large systems by the use of generalized coordinates. An example of a closed-kinematic-chain system is included along with a comparison with the open-dynamics engine (ODE) to illustrate the scalability and desirable energetic properties of the technique. A second example demonstrates an application to an actuated mechanical system.

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.

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.

Stability analysis of decentralized control mechanisms for networked coordinating systems has generally focused on specific controller implementations, such as nearest-neighbor and other types of proximity graph control laws. This approach often misses the need for the addition of other control structures to improve global characteristics of the network. An example of such a situation is the use of a Gabriel graph, which is essentially a nearest-neighbor rule modified to ensure global connectivity of the network if the agents are pairwise connected through their sensor inputs. We present a method of ensuring provable stability of decentralized switching systems by employing a hysteresis rule that uses a zero-sum consensus algorithm. We demonstrate the application of this result to several special cases, including nearest-neighbor control laws, Gabriel graph rules, diffuse target tracking, and hierarchical heterogeneous systems.

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

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

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

This paper develops a formal connection between the power dissipation method (PDM) and Lagrangian mechanics, with specific application to robotic systems. Such a connection is necessary for understanding how some of the successes in motion planning and stabilization for smooth kinematic robotic systems can be extended to systems with frictional interactions and overconstrained systems. We establish this connection using the idea of a multiple-model system, and then show that multiple-model systems arise naturally in a number of instances, including those arising in cases traditionally addressed using the PDM. We then give necessary and sufficient conditions for a dynamic multiple-model system to be reducible to a kinematic multiple-model system. We use this result to show that solutions to the PDM are actually kinematic reductions of solutions to the Euler-Lagrange equations. We are particularly motivated by mechanical systems undergoing multiple intermittent frictional contacts, such as distributed manipulators, overconstrained wheeled vehicles, and objects that are manipulated by grasping or pushing. Examples illustrate how these results can provide insight into the analysis and control of physical systems

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.

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.

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.

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.

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.

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.

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.