This paper presents a new method of generating an optimal approach velocity to control the collision forces between a manipulator and its environment. First, an analysis of the contact motion shows the necessity to control the contact not only after the collision, as shown in previous studies, but also before the collision. Next, using a model of the force-controlled end-effector and its environntent, the forces generated at the contact are formulated as outputs of an autonomous system. In this system, the initial condition is determined by the approach velocity. The optimal approach velocity is defined as the velocity that minimizes the perfonnance index: the integral of the square deviation of the contact forces from the equilibrium force in the control of contact forces. A proportional relation between the optimal approach velocity and the contact force reference is derived analytically based on a mass-damper-spring model of the force-controlled end-effector and its environment. The results of the simulation and experiment demonstrate the effectiveness of the method.
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