Stabilized minimum infinity-norm torque solution for redundant manipulators

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 maximum torques of the actuators are limited. To obtain the minimum ∞-norm torque solution, we devised a new algorithm that uses the acceleration polyhedron representing the end-effector's acceleration capability. Usually the minimization of the joint torques has an instability problem for the long trajectories of the end-effector. To suppress this instability problem, an inequality constraint, named the feasibility constraint, is developed from the geometrical relation between the required end-effector acceleration and the acceleration polyhedron. The minimization of the °-norm of the joint torques subject to the feasibility constraint is shown to improve the performances through the simulations of a 3-link planar redundant manipulator.