Real-time force optimization in parallel kinematic chains under inequality constraints

The real-time control of cooperating manipulators, mechanical hands, and walking machines involves the optimization of an underdetermined force system subject to both equality and inequality constraints. The inequality constraints arise as a result of passive frictional contacts in systems that depend on these for force transmission, or when taking into account the limited torque or force capability of the actuators. Since the results of the force optimization are used to provide force or torque setpoints to the actuators, they must be obtained in real time. A technique is presented for solving a quadratic optimization problem with equality and inequality constraints for this application. The technique is compared with linear programming to show its superior performance in terms of speed and the quality of the solution