Path-constrained Timen-ioptimal Robot Control

Fast movement along a predefined path is important for many robot applications, especially in cluster tool robots, requires utilization of the maximum allowable torque range. Robot running along the time-optimal path brings many benefits such as higher productivity. In this paper, moving a delicate object from an initial point to a specified location along a predefined path within the minimum time under a damage-free condition is studied. To achieve this goal, the dynamics of robot is first described as the formulation using arc differential of the predefined path in Cartesian coordinates. Then, the range of acceleration is deducted from the torque limitations, and the method of computing the maximum and minimum acceleration is given. This range can be modified by consideration of the geometrical constraints. Considering the torque constraint on the object, the range of maximum acceleration and velocity are obtained to preserve object safety while the manipulator is carrying it along the curved path. After that, a method to solve the time-optimal problem is presented, and the detailed process is explained. In this way time-optimal trajectory is planned within the maximum allowable range of acceleration and velocity. This algorithm is implemented on a 2-arm, 2-dof cluster tool robot and its validity is proven by simulation result.