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 for the actuators, they must be obtained in real time. A technique for solving a quadratic optimization problem with equality and inequality constraints is presented for this application. The technique is compared with linear programming schemes to show its superior performance in terms of the speed and quality of the solution. The technique is well suited to problems where the solution can change discontinuously in time, as is the case with the systems considered due to changes in their topology