Optimal approach velocity of end-effector to the environment

A method of generating an optimal approach velocity, to control the collision forces properly, of a manipulator to its environment is presented. Analysis of a contact motion shows the necessity of contact control not only after the collision, but also before it. Using a model of the force-controlled end-effector and its environment, forces generated at the contact are formulated as outputs of an autonomous system of which the initial condition is determined by the approach velocity. The optimal approach velocity is defined as the velocity that minimizes a performance index. 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. Results of the simulation and the experiment are presented to demonstrate the effectiveness of the method.