Constrained Multi-Objective Trajectory Planning of Parallel Kinematic Machines

This paper presents a new approach to multi-objective dynamic trajectory planning of Parallel Kinematic Machines (PKM) under task, workspace and manipulator constraints. The robot kinematic and dynamic models, (including actuators) are first developed. Then the proposed trajectory planning system is introduced. It minimizes electrical and kinetic energy, robot travel time separating two sampling periods and maximizes a measure of manipulability allowing singularity avoidance. Several technological constraints such as actuator limits, link length and workspace bounds, and certain task requirements, such as passing through imposed poses are simultaneously satisfied. The discrete augmented Lagrangian technique is used to solve the resulting non-linear and non-convex constrained optimal control problem. A decoupled formulation is proposed in order to cope with some difficulties arising from dynamic parameters computation. A systematic implementation procedure is provided along with some numerical issues. Simulation results proving the effectiveness of the proposed approach on a 2-degrees of freedom PKM are given and discussed.