An optimal control approach to the design of periodic orbits for mechanical systems with impacts |
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| Affiliation: | 1. School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, PR China;2. School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu 610054, PR China;1. Centre for Research in Automatic Control of Nancy (CRAN), University of Lorraine, France;2. Systems & Control Engineering, Indian Institute of Technology Bombay, Powai, Mumbai - 400076, India;1. School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK;2. School of Earth and Ocean Sciences, Cardiff University, Cardiff CF10 3AT, UK |
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| Abstract: | In this paper we study the problem of designing periodic orbits for a special class of hybrid systems, namely mechanical systems with underactuated continuous dynamics and impulse events. We approach the problem by means of optimal control. Specifically, we design an optimal control based strategy that combines trajectory optimization, dynamics embedding, optimal control relaxation and root finding techniques. The proposed strategy allows us to design, in a numerically stable manner, trajectories that optimize a desired cost and satisfy boundary state constraints consistent with a periodic orbit. To show the effectiveness of the proposed strategy, we perform numerical computations on a compass biped model with torso. |
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| Keywords: | Nonlinear optimal control Trajectory generation Hybrid systems Biped walking |
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