| Although the dynamic equations of motion of open-chained robot systems are well-known, they are seldom taken into account during the planning of motions. In this work, we show that the dynamics of a robot can be taken into account in motion planning. Two applications of dynamic motion planning are explored: (1) development of point-to-point weightlifting motions for open-chained robots; and (2) design of robotic gait rehabilitation. The governing optimal control problem is converted into a direct, SQP parameter optimization in which the gradient is determined analytically. The joint trajectories are defined by B-spline polynomials along with a time-scale factor. In the first application, a weightlifting motion planner is applied to a Puma 762 robot, with its physical limitations incorporated into the formulation. The problem is formulated as an optimal control problem for a fully actuated articulated chain. The torque limits are formulated as soft constraints added into 217, the objective function while the position and velocity limits are formulated as hard, linear inequality constraints, on the parameters. The solutions obtained with the motion planner extend the robot's payload capability while reducing the joint torques. Interestingly, nearly all the trajectories found pass through singular configurations, where large internal forces from the robot are applied to the payload and little torque is needed from the motors. In the second application, we examine a method to control the stepping motion of a paralyzed person suspended on a treadmill using a robot attached to the pelvis. A leg swing motion is created by moving the pelvis without contact with the legs. The problem is formulated as an optimal control problem for an underactuated articulated chain. Motion capture data recorded from an unimpaired human subject is compared to the simulation results from the dynamic motion optimization. Our results suggest that it is feasible to create a gait for a paralyzed person that is close to that of an unimpaired subject by controlling the pelvis with a robot. The resulting motions of the two applications can be found at the web sites “http://www.eng.uci.edu/∼chwang/project/puma762.html” and “http://www.eng.uci.edu/∼chwang/project/stepper/stepper.html”. |
