Stabilization constraint method for torque optimization of a redundant manipulator

The minimization of the joint torques based on the ∞-norm is proposed for the dynamic control of a kinematically redundant manipulator. The ∞-norm is preferred to the 2-norm in the minimization of the joint torques since the torques of the actuators are limited by their maximum values in magnitudes. To obtain the minimum ∞-norm torque solution, we devised a new method that uses the acceleration polyhedron representing the end-effector´s acceleration capability. Usually the torque minimization has the instability problem for the long trajectories of the end-effector. To suppress this instability problem, an inequality constraint, named the stabilization constraint, is developed from geometrical relations between the desired end-effector acceleration and the acceleration polyhedron. The minimization of the ∞-norm of the joint torques subject to the stabilization constraint is shown to improve the performances through the simulations of a 3-link planar redundant manipulator