Kinematic motion constraints in the robot's joint space

In this paper, we investigate the problem of representing the kinematic motion constraints imposed on the robot arm due to the presence of the obstacles. The motion constraints placed on various planar robot arms have been studied using the contact information among the robot arm and the obstacles, we have shown that the kinematic motion constraints caused by any types of obstacles can be analytically and explicitly described by a set of parametric equations. The mapping functions which transfer the obstacles from the work space into the robot's joint space have been derived for four commonly used mechanisms (RR, RP, PR and PP robot arms), respectively. Simulations have been carried out for various planar robot arms to verify the validity of the approach.