A novel approach to the problem of inverse kinematics for redundant manipulators has been recently introduced: by considering the joints as point masses in a fictitious gravity field, and by adding proper constraints to take into account the length of the links, the kinematic inversion may be cast as a convex programming problem. Such a problem can be solved in an efficient way and may be easily modified to include constraints due to obstacles. Here we present further developments of the idea. In particular, for the case of planar robots, we show (i) how to impose hard constraints on the joint angles while preserving the convexity of the problem, and (ii) how to add constraints due to objects (for instance, a load carried by the robot) that are rigidly attached to some part of the robot.
