Minimum-time trajectory planning for multiple manipulators handling an object with geometric path constraints

Presents an approach for optimizing the joint torques on the minimum-time trajectory in the criterion of minimum torque change. The torque change a summation of absolute values of differences between the torques at two discrete points, is a nonlinear function. To avoid the authors nonlinear optimization, the authors introduce a linear objective function which gives the same effect. On the basis of the linear objective function and dynamics of the system which constrains the joint torques and the internal forces between the manipulators and the object linearly, the linear programming approach is used to optimize the joint torques