Optimal control of the rectilinear motion of a rigid body on a rough plane by means of the motion of two internal masses |
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| Authors: | NN Bolotnik TYu Figurina |
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| Institution: | 1. Lincoln Centre for Autonomous Systems (L-CAS), University of Lincoln, Lincoln, LN6 7TS, United Kingdom;2. School of Computer Science and Network Security, Dongguan University of Technology, Dongguan, 523808, China;3. Newcastle Business School, Northumbria University, Newcastle, NE1 8ST, UK;4. Faculty of Science and Technology, Bournemouth University, Poole, BH12 5BB, United Kingdom;1. School of Engineering, Robert Gordon University, Garthdee Road, Aberdeen AB10 7GJ, UK;2. Centre for Applied Dynamics Research, School of Engineering, King?s College, University of Aberdeen, Aberdeen AB24 3UE, UK;3. State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, PR China;1. TU Ilmenau, Department of Mechanical Engineering, Max-Planck-Ring 12, D-98693 Ilmenau, Germany;2. Institute for Problems in Mechanics of the Russian Academy of Sciences, 101 bld. 1 Vernadskii Ave, Moscow 119526, Russia |
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| Abstract: | The problem of the optimal control of a rigid body moving along a rough horizontal plane due to motion of two internal masses is solved. One of the masses moves horizontally parallel to the line of motion of the main body, while the other mass moves in the vertical direction. Such a mechanical system models a vibration-driven robot–a mobile device able to move in a resistive medium without special propellers (e.g., wheels, legs or caterpillars). Periodic motions are constructed for the internal masses to ensure velocity-periodic motion of the main body with maximum average velocity, provided that the period is fixed and the magnitudes of the accelerations of the internal masses relative to the main body do not exceed prescribed limits. Based on the optimal solution obtained for a fixed period without any constraints imposed on the amplitudes of vibration of the internal masses, a suboptimal solution that takes such constraints into account is constructed. |
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