In a cooperating multiple robot manipulator system, joint actuators which drive the multiple robot system are redundantly equipped in general because each manipulator can operate a given motion holding an object without being assisted by other robot manipulators. Therefore, the joint torques to carry out a given task are not uniquely determined due to the redundancy of joint actuators. The redundancy of joint actuators can be used for many objectives such as the minimization of exerted energy or the safeguard of weak points. The problem to resolve this redundancy is called a force distribution problem or a load distribution problem.
This paper discribes a force distribution method which minimizes some objective functions and satisfies equality and inequality constraints. The proposed method is to prevent the damage or unwanted motion of any weak points such as points on weak links, joints, end-effectors, a long and narrow object, weakly assembled parts, and very large objects on robot manipulators and/or an object from the excessive forces/torques exerted at these points. The objective function can be one of the following types: linear function, one-norm, two-norm, or infinite-norm of weak point forces. Since weak points defined in this paper are generalized one which can be any critical points and/or interesting points, an objective function and constraints can be expressed as a function of weak point force. To solve the force distribution problem weak point forces are represented as a function of the forces exerted at end-effectors and then an objective function is transformed to the function of end-effector forces. After transformation, the optimum end-effector forces are obtained by minimizing the objective function under equality and inequality constraints.
For the case that weak points cannot be safeguarded by the proposed force distribution method from excessive forces, a new trajectory by which weak points can be safeguarded are required. And one of the most important matters in industrial applications is that a given must be carried out as soon as possible. Therefore, a minimum time trajectory planning method is proposed in this paper. For the minimum time trajectory planning, inequality constraints for weak points are constructed as a function of a parameterized path. Since the minimum time trajectory is constructed by the association of the maximum acceleration curves and maximum deceleration curves, maximum acceleration curves and maximum deceleration curves satisfying the inequality constraints are constructed using a linear programming method. An interconnection scheme to connect the maximum acceleration curves and the maximum deceleration curves are proposed in order that the resulting trajectory can be directly applied for computer aided digital control.
The proposed force distribution and minimum time trajectory planning methods are simulated using two identical PUMA 560 robot manipulators holding an object to illustrate the method. The proposed method is applicable to diverse areas such as handling a fragile and ling object, weakly connected assembly parts, long links, and weakly combined joints in cooperating multiple robots system. Also these methods are applicable to a multi-legged vehicle and a multi-fingered hand, whose characteristics are analogous to the cooperating multiple robot manipulator system.
