We examine a method to control the stepping motion of a paralyzed person suspended on a treadmill using a robot attached to the torso and hips. A leg swing motion is created by moving the hips without contact with the legs. The problem is formulated as an optimal control problem for an underactuated articulated chain. The optimal control problem is converted into a discrete parameter optimization and an efficient gradient-based algorithm is used to solve it. Motion capture data from a human subject is compared to the results from the dynamic motion optimization. Our results indicate that it is possible for the robot to create a gait for the paralyzed person that is close to that of an unimpaired subject.

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 used to produce motions that extend the payload capability beyond the limit set by traditional methods. In particular, we develop a point-to-point weightlifting motion planner for open-chained robots. 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. The algorithm is applied to a Puma 762 robot, with its physical limitations incorporated into the formulation. The torque limits are formulated as soft constraints added into the objective function while the position and velocity limits are formulated as hard, linear inequality constraints, on the parameters. The solutions obtained with our algorithm 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 this paper we develop a point-to-point weight lifting motion planner for open-chained robots. The joint trajectories are defined by B-spline polynomials along with a time-scale factor. Physical limitations of a Puma 762 robot are incorporated into the formulation. The torque limits are formulated as a penalty function (soft constraints) added into the objective function while the position and velocity limits are formulated as linear inequalities (hard constraints). The problem is solved by a gradient-based optimization method in which the gradient is determined analytically. Not only does the optimal path extend the payload capability, but also reduces the joint torques by passing through singular configurations.