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Task-level control of the Lateral Leg Spring model of cockroach locomotion

引用

Symposium on Fast Motions in Biomechanics and Robotics

作者： Lee, J. Lamperski, A. Schmitt, J. Cowan, N. Johns Hopkins Univ Baltimore MD 21218 USA CALTECH Pasadena CA 91125 USA Oregon State Univ Corvallis OR 97331 USA

ISBN: (纸本)3540361189

The Lateral Leg Spring model (LLS) was developed by Schmitt and Holmes to model the horizontal-plane dynamics of a running cockroach. The model captures several salient features of real insect locomotion, and demonstrates that horizontal plane locomotion can be passively stabilized by a well-tuned mechanical system, thus requiring minimal neural reflexes. We propose two enhancements to the LLS model. First, we derive the dynamical equations for a more flexible placement of the center of pressure (COP), which enables the model to capture the phase relationship between the body orientation and center-of-mass (COM) heading in a simpler manner than previously possible. Second, we propose a reduced LLS "plant model" and biologically inspired control law that enables the model to follow along a virtual wall, much like antenna-based wall following in cockroaches.

关键词： Antennas

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Running and walking with compliant legs

引用

Symposium on Fast Motions in Biomechanics and Robotics

作者： Seyfarth, A. Geyer, H. Blickhan, R. Lipfert, S. Rummel, J. Minekawa, Y. Iida, F. Univ Jena Locomot Lab D-07743 Jena Germany Univ Jena D-07749 Jena Germany Univ Zurich Artificial Intelligence Lab CH-8050 Zurich Switzerland

ISBN: (纸本)3540361189

It has long been the dream to build robots which could walk and run with ease. To date, the stance phase of walking robots has been characterized by the use of either straight, rigid legs, as is the case of passive walkers, or by the use of articulated, kinematically-driven legs. In contrast, the design of most hopping or running robots is based on compliant legs which exhibit quite natural behavior during locomotion. Here we ask to what extent spring-like leg behavior could be useful in unifying locomotion models for walking and running. In so doing, we combine biomechanical experimental and computer simulation approaches with theoretical considerations and simple legged robots. We have found that (1) walking and running result from mechanical stability which corresponds to the experimentally observed gait dynamics, (2) running is a subset of stable movement patterns for high system energies, and (3) walking with knee flexion during stance can result from passive leg mechanics with elastic structures spanning the joints.

关键词： Mechanical stability

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An approximate dynamic programming approach to decentralized control of stochastic systems

引用

Workshop on control of Uncertain Systems

作者： Cogill, R Rotkowitz, M Van Roy, B Lall, S Stanford Univ Dept Elect Engn Stanford CA 94305 USA Stanford Univ Dept Aeronaut & Astronaut Stanford CA 94305 USA Stanford Univ Dept Management Sci & Engn Stanford CA 94305 USA Stanford Univ Dept Elect Engn Stanford CA 94305 USA Stanford Univ Dept Aeronaut & Astronaut Stanford CA 94305 USA

ISBN: (纸本)3540317546

We consider the problem of computing decentralized control policies for stochastic systems with finite state and action spaces. Synthesis of optimal decentralized policies for such problems is known to be NP-hard [1]. Here we focus on methods for efficiently computing meaningful suboptimal decentralized' control policies. The algorithms we present here are based on approximation of optimal Q-functions. We show that the performance loss associated with choosing decentralized policies with respect to an approximate Q-function is related to the approximation error.

关键词： Decentralized control

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Multi-locomotion control of biped locomotion and brachiation robot

引用

Symposium on Fast Motions in Biomechanics and Robotics

作者： Fukuda, T. Doi, M. Hasegawa, Y. Kajima, H. Nagoya Univ Dept Micronano Syst Engn Chikusa Ku Nagoya Aichi 4648603 Japan Univ Tsukuba Dept Intelligent Interact Technol Tsukuba Ibaraki 3058573 Japan

ISBN: (纸本)3540361189

This paper first introduces a multi-locomotion robot with high mobility and then proposes Passive Dynamic Autonomous control (PDAC) for the comprehensive control method of multiple types of locomotion. PDAC is the method to take advantage of the robot inherent dynamics and to realize natural dynamic motion. We apply PDAC to a biped walk control. On the assumption that the sagittal and lateral motion can be separated and controlled individually, each motion is designed based on the given desired step-length and period. In order to stabilize walking, the landing position control according to the status is designed. In addition, a coupling method between these motions, which makes the period of each motion identical, is proposed. Finally, we show that the multi-locomotion robot realizes the 3-dimensional dynamic walking using the PDAC control.

关键词： Position control

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Recent advances on the algorithmic optimization of robot motion

引用

Symposium on Fast Motions in Biomechanics and Robotics

作者： Bobrow, J. E. Park, F. C. Sideris, A. Univ Calif Irvine Dept Mech & Aerosp Engn Irvine CA 92697 USA

ISBN: (纸本)3540361189

An important technique for computing motions for robot systems is to conduct a numerical search for a trajectory that minimizes a physical criteria like energy, control effort, jerk, or time. In this paper, we provide example solutions of these types of optimal control problems, and develop a framework to solve these problems reliably. Our approach uses an efficient solver for both inverse and forward dynamics along with the sensitivity of these quantities used to compute gradients, and a reliable optimal control solver. We give an overview of our algorithms for these elements in this paper. The optimal control solver has been the primary focus of our recent work. This algorithm creates optimal motions in a numerically stable and efficient manner. Similar to sequential quadratic programming for solving finite-dimensional optimization problems, our approach solves the infinite-dimensional problem using a sequence of linear-quadratic optimal control subproblems. Each subproblem is solved efficiently and reliably using the Riccati differential equation.

关键词： Quadratic programming

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Simple feedback control of cockroach running

引用

Symposium on Fast Motions in Biomechanics and Robotics

作者： Schmitt, J. Oregon State Univ Corvallis OR 97331 USA

ISBN: (纸本)3540361189

The spring loaded inverted pendulum model (SLIP) has been shown to accurately model sagittal plane locomotion for a variety of legged animals. Tuned appropriately, the model exhibits passively stable periodic gaits using either fixed leg touchdown angle or swing-leg retraction protocols. In this work, we investigate the relevance of the model in insect locomotion and develop a simple feedback control law to enlarge the basin of stability and produce stable periodic gaits for both the point mass and rigid body models. control is applied once per stance phase through appropriate choice of the leg touchdown angle. The control law is unique in that stabilization is achieved solely through direct observation of the leg angle and body orientation, rather than through feedback of system positions, velocities, and orientation.

关键词： Feedback control

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Investigating the use of iterative learning control and repetitive control to implement periodic gaits

引用

Symposium on Fast Motions in Biomechanics and Robotics

作者： Longman, R. W. Mombaur, K. D. Columbia Univ Dept Mech Engn New York NY 10027 USA Heidelberg Univ IWR D-69120 Heidelberg Germany

ISBN: (纸本)3540361189

In the next few years considerable effort will be expended to make humanoid robots that can do true dynamic walking, or even running. One may numerically compute a desired gait, e.g. one that has been optimized to be asymptotically stable without feedback. One would normally give the gait as commands to the controllers for the robot joints. However, control system outputs generally differ from the command given, and the faster the command changes with time, the more deviation there is. Iterative learning control (ILC) and repetitive control (RC) aim to fix this problem in situations where a command is repeating or periodic. Since gaits are periodic motions, it is natural to ask whether ILC/RC can be of use in implementing gaits in hardware. These control concepts are no substitutes for feedback control but work in combination with them by adjusting the commands to the feedback controllers from a higher level perspective. It is shown that the gait problem does not precisely fit either the ILC or the RC problem statements. Gait problems are necessarily divided into phases defined by foot strike times, and furthermore the durations of the phases are not the same from cycle to cycle during the learning process. Several methods are suggested to address these issues, and four repetitive control laws axe studied numerically. The laws that include both position and velocity error in the updates are seen to be the most effective. It appears that with appropriate refinement, such generalized RC laws could be very helpful in getting hardware to execute desired gaits.

关键词： Feedback control

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Nonlinear model predictive control and sum of squares techniques

引用

Symposium on Fast Motions in Biomechanics and Robotics

作者： Raff, T. Ebenbauer, C. Findeisen, R. Allgoewer, F. Univ Stuttgart Inst Syst Theory & Automat Control D-7000 Stuttgart Germany

ISBN: (纸本)3540361189

The paper considers the use of sum of squares techniques in nonlinear model predictive control. To be more precise, sum of squares techniques are used to solve at each sampling instant a finite horizon optimal control problem which arises in nonlinear model predictive control for discrete time polynomial systems. The combination of nonlinear model predictive control and sum of squares techniques is motivated by the successful application of semidefinite programming in linear model predictive control. The advantages and disadvantages of applying sum of squares techniques to nonlinear model predictive control are illustrated on a small example.

关键词： Model predictive control

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Dynamical synthesis of a walking cyclic gait for a biped with point feet

引用

Symposium on Fast Motions in Biomechanics and Robotics

作者： Miossec, S. Aoustin, Y. Natl Inst Adv Ind Sci & Technol AIST Intelligent Syst Res Inst Joint Japanese French Robot Lab Tsukuba Ibaraki 3058568 Japan Univ Nantes Ecole Cent Nantes CNRS Inst Rech Commun & Cybernet NantesUMR 6597 F-44321 Nantes 3 France

ISBN: (纸本)3540361189

This paper deals with a methodology to design optimal reference trajectories for walking gaits. This methodology consists of two steps: (i) design a parameterized family of motions, and (ii) determine the optimal parameters giving the motion that minimizes a criterion and satisfies some constraints within this family. This approach is applied to a five link biped, the prototype Rabbit. It has point feet and four actuators which are located in each knee and haunch. Rabbit is underactuated in single support since it has no actuated feet and is overactuated. in double support. To take into account this under-actuation, a characteristic of the family of motions considered is that the four actuated joints are prescribed as polynomials in function of the absolute orientation of the stance ankle. There is no impact. The chosen criterion is the integral of the square of torques. Different technological and physical constraints are taken into account to obtain a walking motion. Optimal process is solved considering an order of treatment of constraints, according to their importance on the feasibility of the walking gait. Numerical simulations of walking gaits are presented to illustrate this methodology.

关键词： Robotics

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On the gap metric for finite-dimensional linear time-varying systems in continuous time

引用

Workshop on control of Uncertain Systems

作者： Cantoni, M Univ Melbourne Dept Elect & Elect Engn Parkville Vic 3010 Australia

ISBN: (纸本)3540317546

It is well-known that the gap metric, and its variants, provide a natural framework for studying the robustness of feedback interconnections [1–4]. In fact, for arbitrary linear systems, it is known that the gap metric induces the weakest topology in which both feedback stability and closed-loop performance are both robust properties [5]. In this article, we study the gap metric for the class of finite-dimensional, linear time-varying systems, in continuous-time. In particular, it is shown that the gap between two systems is equal to the norm of an operator composed of normalised left and right representations of the system graphs. The development relies on tools familiar from the time-invariant setting. This is in contrast to the abstract results which underpin the discretetime generalisations of the gap framework to the time-varying setting [6,7]. Using ideas from [8,9], an alternative characterisation of the gap is also established in terms of a standard linear fractional synthesis problem from robust control theory. This characterisation appears to be useful for approximation in the gap, and might be extendable to other classes of system. © Springer-Verlag Berlin Heidelberg 2006.

关键词： non-autonomous differential equations gap metric Riccati equations (J-)spectral factorisation robust control approximation

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