Optimal Balancing of Spatial Suspended Cable Robot in Point-to-Point Motion using the Indirect Approach

In this paper, a method based on the indirect solution of optimal control problem is presented to specify the optimal trajectory of spatially suspended cable robot in point to point motion with considering the counterweights. In fact, an optimal trajectory planning problem is outlined in which states, controls and the values of counterweights must be calculated simultaneously in order to minimize the given performance index. The value of the pulley torques is considered for the performance index (objective function). Using the fundamental theorem of a calculus of variations, the necessary conditions for optimality of cable robot are achieved. For the three cable spatial robot, a two-point boundary value problem is achieved which can be solved with bvp4c command in MATLAB. The obtained results show that optimal balancing in comparison with the unbalancing method can reduce the performance index significantly.