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Titlebook: Control Design and Analysis for Underactuated Robotic Systems; Xin Xin,Yannian Liu Book 2014 Springer-Verlag London 2014 Energy- and Passi

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Directly Driven Acrobot,the closed-loop system. Furthermore, imposing a stronger condition on a control parameter yields that the equilibrium set contains only the downward equilibrium point, which is shown to be a saddle. This proves that the DDA will eventually enter the basin of attraction of any stabilizing controller
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Rotational Pendulum,ure zero. This chapter not only validates the presented theoretical results via numerical simulation but also verifies experimentally by using the rotational pendulum system developed by Quanser Inc. The obtained numerical simulation and experimental results show that the presented energy-based swin
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2-Link Underactuated Robot with Flexible Elbow Joint,and analyzes the motion of the robot under the presented controller by studying the convergence of the total mechanical energy and clarifying the structure and stability of the closed-loop equilibrium points. It presents numerical simulation results to validate the obtained theoretical results.
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3-Link Planar Robot with Passive First Joint, on control parameters for achieving the swing-up control objective. To validate the theoretical results obtained, this chapter provides simulation results for a 3-link robot with its mechanical parameters being obtained from a human gymnast.
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,-Link Planar Robot with Passive First Joint,controller and establish conditions on the control parameters that ensure attainment of the swing-up control objective; specifically, it determines the relationship between the closed-loop equilibrium points and a control parameter. Finally, it verifies the theoretical results by means of simulation
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