Repeated Collision of a Planar Robotic Arm with a Surface Using Generalized Active Forces

Abstract

The periodic impact of a planar two-arm robot is investigated in this study. Lagrange’s equations of motion are developed, and the symbolic expression of the generalized active forces are used for the control torques. The actuator torques derived with generalized active forces are compared with PD and PID controllers. The robot collides with a rebound on a rough surface. Different nonlinear functions describe the three stages of the impact: elastic compression, elasto-plastic compression, and elastic restitution. A Coulomb model describes the friction force and the sliding velocity at the impact point. At the end of the impact period, the kinetic energy of the non-impacting link is increasing, and the total kinetic energy of the robot decreases. The motion of the robot with generalized active forces controllers is periodic. The important implication of this study is the generalized forces controller and the impact with friction for the periodic robot.