Manipulating robots along helical trajectories

Current industrial robots arc highly non-linear systems. However, the control strategies in most commercially available robots largely ignore the non-linearity. The resulting linear approximations are only valid at low speeds. Any improvement would allow robots to move faster and hence be more productive. There has been much academic research into robot control, but this has almost always separated the control and the trajectory planning. In this work we seek to combine these tasks and hence simplify the computations required. We investigate how to control a general robot in such a way that it's gripper follows straight line, circular or helical paths. These simple paths are both one parameter subgroups for the group of proper rigid motions and geodesics for certain metrics on the group. This suggests a non-linear feedback control law which turns the closed loop dynamics of the robot into the equations for geodesics. Although these equations are not completely stable we are able to modify the control law so that the resulting closed loop dynamics are stable. Hence, the end-effector of the robot will follow straight line, helical or circular trajectories