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The development of legged robots capable of navigating in and interacting with the world is quickly advancing as new methods and techniques for sensing, decision-making, and controls expand the capabilities of state-of-the-art systems. Model-based methods, empowered by greater computing capacity and clever formulations, are imbuing systems with further physics-based understanding. While machine learning techniques, enabled by parallelized data generation and more efficient training, are imparting greater robustness to noise and abilities to handle poorly defined world features. Together these tools constitute the two major paradigms of legged robot research and while both have their shortcomings, they have complementary limitations that can be reinforced by the other's strengths. We propose MIMOC: Motion Imitation from Model-Based Optimal Control. MIMOC is a Reinforcement Learning (RL) locomotion controller that learns agile locomotion by imitating reference trajectories from model-based optimal control. MIMOC mitigates challenges faced by other motion imitation-based RL approaches because the generated reference trajectories are dynamically consistent, require no motion retargeting, and include torque references that are essential to learn dynamic locomotion. As a result, MIMOC does not require any fine-tuning to transfer the policy to the real robots. MIMOC also overcomes key issues with model-based optimal controllers. Since it is trained with simulated sensor noise and domain randomization, MIMOC is less sensitive to modeling and state estimation inaccuracies. We validate MIMOC on the Mini-Cheetah in outdoor environments over a wide variety of challenging terrain and on the MIT Humanoid in simulation. We show that MIMOC can transfer to the real-world and to different legged platforms. We also show cases where MIMOC outperforms model-based optimal controllers, and demonstrate the value of imitating torque references.
Bioinspired Legged Locomotion: Models, Concepts, Control and Applications explores the universe of legged robots, bringing in perspectives from engineering, biology, motion science, and medicine to provide a comprehensive overview of the field. With comprehensive coverage, each chapter brings outlines, and an abstract, introduction, new developments, and a summary. Beginning with bio-inspired locomotion concepts, the book's editors present a thorough review of current literature that is followed by a more detailed view of bouncing, swinging, and balancing, the three fundamental sub functions of locomotion. This part is closed with a presentation of conceptual models for locomotion. Next, the book explores bio-inspired body design, discussing the concepts of motion control, stability, efficiency, and robustness. The morphology of legged robots follows this discussion, including biped and quadruped designs. Finally, a section on high-level control and applications discusses neuromuscular models, closing the book with examples of applications and discussions of performance, efficiency, and robustness. At the end, the editors share their perspective on the future directions of each area, presenting state-of-the-art knowledge on the subject using a structured and consistent approach that will help researchers in both academia and industry formulate a better understanding of bioinspired legged robotic locomotion and quickly apply the concepts in research or products. Presents state-of-the-art control approaches with biological relevance Provides a thorough understanding of the principles of organization of biological locomotion Teaches the organization of complex systems based on low-dimensional motion concepts/control Acts as a guideline reference for future robots/assistive devices with legged architecture Includes a selective bibliography on the most relevant published articles
Both optimal control methods and learning-based methods have been widely used for the control of legged locomotion. While optimal control formulations allow the designer to guarantee constraints on the solutions found, learning-based methods can leverage data and past experiences to globally search for solutions robust to noise and errors in the model parameters. This work explores how optimal control methods can be guided and structured by using data-driven techniques such as supervised learning and Bayesian optimization. Two case studies are presented. The first presents a model predictive controller for quadrupedal landing that reasons about body states, reaction forces, and contact timings in an online fashion. This highly nonlinear problem is made tractable by collecting thousands of feasible trajectories offline from trajectory optimizations and learning to generate them from the initial falling conditions. By initializing the search for a solution with the approximation from a deep neural network, the MIT Mini Cheetah is shown to be able to recover from significant falls in simulation and hardware in real time. The second studies the effect of learning command-dependent weights for a convex model predictive controller. The weights for the running costs are adjusted dynamically as a function of the command input. Using black-box optimization techniques and a defined higher-level reward, a function mapping the command input to the weights can be determined by sampling the trajectories from sweeps of command inputs.
A variety of impressive approaches to legged locomotion exist; however, the science of legged robotics is still far from demonstrating a solution which performs with a level of flexibility, reliability and careful foot placement that would enable practical locomotion on the variety of rough and intermittent terrain humans negotiate with ease on a regular basis. In this thesis, we strive toward this particular goal by developing a methodology for designing control algorithms for moving a legged robot across such terrain in a qualitatively satisfying manner, without falling down very often. We feel the definition of a meaningful metric for legged locomotion is a useful goal in and of itself. Specifically, the mean first-passage time (MFPT), also called the mean time to failure (MTTF), is an intuitively practical cost function to optimize for a legged robot, and we present the reader with a systematic, mathematical process for obtaining estimates of this MFPT metric. Of particular significance, our models of walking on stochastically rough terrain generally result in dynamics with a fast mixing time, where initial conditions are largely "forgotten" within 1 to 3 steps. Additionally, we can often find a near-optimal solution for motion planning using only a short time-horizon look-ahead. Although we openly recognize that there are important classes of optimization problems for which long-term planning is required to avoid "running into a dead end" (or off of a cliff!), we demonstrate that many classes of rough terrain can in fact be successfully negotiated with a surprisingly high level of long-term reliability by selecting the short-sighted motion with the greatest probability of success. The methods used throughout have direct relevance to machine learning, providing a physics-based approach to reduce state space dimensionality and mathematical tools to obtain a scalar metric quantifying performance of the resulting reduced-order system.
In this study artificial neural networks and fuzzy logic are used to control the jumping behavior of a three-link uniped robot. The biped locomotion control problem is an increment of the uniped locomotion control. Study of legged locomotion dynamics indicates that a hierarchical controller is required to control the behavior of a legged robot. A structured control strategy is suggested which includes navigator, motion planner, biped coordinator and uniped controllers. A three-link uniped robot simulation is developed to be used as the plant. Neurocontrollers were trained both online and offline. In the case of on-line training, a reinforcement learning technique was used to train the neurocontroller to make the robot jump to a specified height. After several hundred iterations of training, the plant output achieved an accuracy of 7.4%. However, when jump distance and body angular momentum were also included in the control objectives, training time became impractically long. In the case of off-line training, a three-layered backpropagation (BP) network was first used with three inputs, three outputs and 15 to 40 hidden nodes. Pre-generated data were presented to the network with a learning rate as low as 0.003 in order to reach convergence. The low learning rate required for convergence resulted in a very slow training process which took weeks to learn 460 examples. After training, performance of the neurocontroller was rather poor. Consequently, the BP network was replaced by a Cerebeller Model Articulation Controller (CMAC) network. Subsequent experiments described in this document show that the CMAC network is more suitable to the solution of uniped locomotion control problems in terms of both learning efficiency and performance. A new approach is introduced in this report, viz., a self-organizing multiagent cerebeller model for fuzzy-neural control of uniped locomotion is suggested to improve training efficiency. This is currently being evaluated for a possible ...
Legged animals have explored more of the Earth's surface than any human designed vehicle. The agility, adaptability, and efficiency found in nature continues to inspire robotics researchers to develop efficient leg designs robust, stable and adaptable control strategies that can rapid changes in the environment. Understanding the dynamics of ground collision and contact is critical to advancing the state of the art of legged robotics and allowing legged robotics to narrow the performance gap with legged animals. Unfortunately modeling the dynamics of collision requires attention not just to whole cycle measures like the coefficient of restitution but also to the transient measures of slip and initiation of chatter. This thesis contributes to the model-based design and control of legged robots by developing compliant contact models for systems where the deformation of the contact bodies is small and the contact forces can be considered to act through a single point. A novel visco-plastic contact model is developed to represent collision dynamics during legged locomotion. The relationship between the model's damping parameter and the coefficient of restitution is formulated using the energetic coefficient which permits energy consistent formulation for collisions that are non-collinear and include slip reversal. Given experimental data of the position and force of the foot, the model parameter estimation is performed with an offline genetic algorithm and an online unscented Kalman filter. The effectiveness of the methods are demonstrated on one-dimensional collisions of a single mass and a mass spring damper system. The methods presented allow for a physics-based study of the effect of leg and foot compliance on the energy efficiency of legged locomotion and of locomotion controllers. An actuated, non conservative, continuous contact SLIP model is developed for greater analysis of dynamics of running. Methodologies for finding passive (and active) gait controllers are of great interest to robotics but for non-conservative models, there are no passively stable fixed points around which to build such controllers. Minimal heuristic controllers are generated for bouncing gait generation which allow for stable hopping in the presence of actuator and ground contact energy losses. Together with the online inverse model parameter estimation, the approach advances robotics toward realizing adaptive optimal efficiency locomotion based on terrain measurements.
Terrestrial animals encounter natural surfaces which comprise materials that can yield and flow such as sand, rubble, and debris, yet appear to nimbly walk, run, crawl, or climb across them with great ease. In contrast, man-made devices on wheels and treads suffer large performance loss on these surfaces. Legged locomotion thus provides an excellent source of inspiration for creating devices of increased locomotor capabilities on natural surfaces. While principles of legged locomotion on solid ground have been discovered, the mechanisms by which legged animals move on yielding/flowing surfaces remain poorly understood, largely due to the lack of fundamental understanding of the complex interactions of body/limbs with these substrates on the level of the Navier-Stokes Equations for fluids. Granular media (e.g., sand) provide a promising model substrate for discovering the principles of legged locomotion on yielding/flowing surfaces, because they can display solid- and fluid-like behaviors, are directly relevant for many desert-dwelling animals, can be repeatably and precisely controlled, and the intrusion force laws can be determined empirically. In this dissertation, we created laboratory devices to prepare granular media in well-controlled states, and integrated biological, robotic, and physics studies to discover principles of legged locomotion on granular media. For both animals and bio-inspired robots, legged locomotion on granular surfaces must be achieved by limb intrusion to generate sufficient vertical ground reaction force (lift) to balance body weight and inertial force. When limb intrusion was slow (speed
A novel Policy Regularized Model Predictive Control (PR-MPC) framework is developed to allow general robust legged locomotion with the MIT Cheetah quadruped robot. The full system is approximated by a simple control model that retains the key nonlinearities characteristic to legged contact dynamics while reducing the complexity of the continuous dynamics. Nominal footstep locations and feedforward forces for controlling the robot's center of mass are designed from simple physics-based heuristics for steady state legged movement. By regularizing the predictive optimization with these policies, we can exploit the known dynamics of the system to bias the controller towards the steady state gait while remaining free to explore the cost space during transient behaviors and disturbances. The nonlinear optimization makes use of direct collocation on the simplified dynamics to pose the problem with a highly sparse structure for fast computation. A generalized approach to the controller design is independent from specific gait pattern and reference policy and allows stabilization of aperiodic locomotion. Simulation results show dynamic capabilities in a variety of gaits including trotting, bounding, and galloping, all without changing the set of algorithm parameters between experiments. Robustness to sensor and input noise, large push disturbances, and unstructured terrain demonstrate the ability of the predictive controller to adapt to uncertainty.
Walking machines have advantages over traditional vehicles, and have already accomplished tasks that wheeled or tracked robots cannot handle. Nevertheless, their use in industry and services is currently limited in scope. This book brings together methods and techniques that have been developed to deal with obstacles to wider acceptance of legged robots. Part I provides an historical overview. Part II concentrates on control techniques, as applied to Four-legged robots.