Guaranteed in-the-workspace improved trajectory/surface/volume verification for parallel robots

The workspace of a parallel robot has a complex shape and is difficult to model. Hence verifying if an arbitrary trajectory lies entirely within this workspace is a complex issue. We present an algorithm that allow such verification for any trajectory such that the pose parameters are arbitrary analytical time function. The proposed algorithm allows to check very quickly the validity of almost any trajectory (or of a surface/volume) in a guaranteed manner. Furthermore this algorithm allows one to deal with uncertainties in the followed trajectory and in the geometrical description of the robot.