433 research outputs found

    Discrete Mechanics and Optimal Control Applied to the Compass Gait Biped

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    This paper presents a methodology for generating locally optimal control policies for simple hybrid mechanical systems, and illustrates the method on the compass gait biped. Principles from discrete mechanics are utilized to generate optimal control policies as solutions of constrained nonlinear optimization problems. In the context of bipedal walking, this procedure provides a comparative measure of the suboptimality of existing control policies. Furthermore, our methodology can be used as a control design tool; to demonstrate this, we minimize the specific cost of transport of periodic orbits for the compass gait biped, both in the fully actuated and underactuated case

    Immersion and invariance orbital stabilization of underactuated mechanical systems with collocated pre-feedback

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    In this note we study the generation of attractive oscillations of a class of mechanical systems with underactuation one. The proposed design consists of two terms, i.e., a partial linearizing state feedback, and an immersion and invariance orbital stabilization controller. The first step is adopted to simplify analysis and design, however, bringing an additional difficulty that the model loses its Euler-Lagrange structure after the collocated pre-feedback. To address this, we propose a constructive solution to the orbital stabilization problem via a smooth controller in an analytic form, and the model class identified in the paper is characterized via some easily apriori verifiable assumptions on the inertia matrix and the potential energy function

    Trajectory stabilization for a planar carangiform robot fish

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    Considers the task of trajectory stabilization for a fish-like robot by means of feedback. We use oscillatory control inputs and apply correction signals at the endpoints of each periodic input signal. Such a strategy can be proven to cause the system to converge to a desired trajectory. We present a specific model of a planar carangiform fish, and verify the stabilization results with simulations and with experiment on a planar robotic fish system that is propelled using carangiform-like movements

    Underwater locomotion from oscillatory shape deformations

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    This paper considers underwater propulsion that is generated by variations in body shape. We summarize and extend some of the emerging approaches for the uniform modeling and control of such underactuated systems. Two examples illustrate these ideas

    Dynamic Walking: Toward Agile and Efficient Bipedal Robots

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    Dynamic walking on bipedal robots has evolved from an idea in science fiction to a practical reality. This is due to continued progress in three key areas: a mathematical understanding of locomotion, the computational ability to encode this mathematics through optimization, and the hardware capable of realizing this understanding in practice. In this context, this review article outlines the end-to-end process of methods which have proven effective in the literature for achieving dynamic walking on bipedal robots. We begin by introducing mathematical models of locomotion, from reduced order models that capture essential walking behaviors to hybrid dynamical systems that encode the full order continuous dynamics along with discrete footstrike dynamics. These models form the basis for gait generation via (nonlinear) optimization problems. Finally, models and their generated gaits merge in the context of real-time control, wherein walking behaviors are translated to hardware. The concepts presented are illustrated throughout in simulation, and experimental instantiation on multiple walking platforms are highlighted to demonstrate the ability to realize dynamic walking on bipedal robots that is agile and efficient

    Trajectory Optimization and Machine Learning to Design Feedback Controllers for Bipedal Robots with Provable Stability

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    This thesis combines recent advances in trajectory optimization of hybrid dynamical systems with machine learning and geometric control theory to achieve unprecedented performance in bipedal robot locomotion. The work greatly expands the class of robot models for which feedback controllers can be designed with provable stability. The methods are widely applicable beyond bipedal robots, including exoskeletons, and prostheses, and eventually, drones, ADAS, and other highly automated machines. One main idea of this thesis is to greatly expand the use of multiple trajectories in the design of a stabilizing controller. The computation of many trajectories is now feasible due to new optimization tools. The computations are not fast enough to apply in the real-time, however, so they are not feasible for model predictive control (MPC). The offline “library” approach will encounter the curse of dimensionality for the high-dimensional models common in bipedal robots. To overcome these obstructions, we embed a stable walking motion in an attractive low-dimensional surface of the system's state space. The periodic orbit is now an attractor of the low-dimensional state-variable model but is not attractive in the full-order system. We then use the special structure of mechanical models associated with bipedal robots to embed the low-dimensional model in the original model in such a manner that the desired walking motions are locally exponentially stable. The ultimate solution in this thesis will generate model-based feedback controllers for bipedal robots, in such a way that the closed-loop system has a large stability basin, exhibits highly agile, dynamic behavior, and can deal with significant perturbations coming from the environment. In the case of bipeds: “model-based” means that the controller will be designed on the basis of the full floating-base dynamic model of the robot, and not a simplified model, such as the LIP (Linear Inverted Pendulum). By “agile and dynamic” is meant that the robot moves at the speed of a normal human or faster while walking off a curb. By “significant perturbation” is meant a human tripping, and while falling, throwing his/her full weight into the back of the robot.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145992/1/xda_1.pd
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