Path optimization for an unilaterally constrained robot arm

The paper deals with the problem to optimize the path of a robot arm being mounted on a mobile platform, which is constrained to the environment by unilateral constraints. The goal is to minimize the needed time as well as the energy consumption under the boundary condition to avoid a change in the state of contact at the unilateral contraints. The contact behaviour of the system is described with a linear complementarity problem LCP. For its solution a compact spatial formulation of Signorini's law is used. The temporal courses of the joint angle velocities are described by ramp functions. The ramp parameters are used as the optimization parameters. Therewith it is possible to vary the different phases of acceleration and constant movement for each joint separately, enabling the optimization algorithm to find an optimal temporal course for the robot's kinematic quantities.