Resolution of redundancy using local optimization : synergy approach

Abstract

Some complex industrial – and especially nonindustrial tasks – induced recently a new approach to robot design and control in order to achieve very stable, fast, and accurate systems. For a example, this is industrial assembly, high speed manipulation, robotized surgery, etc. Such demanding tasks could efficiently be solved if robot was configured as redundant. A redundant robots are called kinematically redundant if they have more degrees of freedom (DOF) then required for a realization of a prescribed task in a task space . The main difficulty of redundant robots is that the task cannot define the joint motions uniquely. For solving this problem, several technical cost functions were proposed. The other idea is to imitate human behavior. Thus, it is necessary to examine the way humans perform complex motions, find the biological analog, and apply it the robot. But, redundant mechanisms also have a disadvantage of the difficulty in controlling them. The main question is how to choose a suitable mechanism configuration from the infinite number of possible configurations called “self-motions” which match each position of the manipulation object, for a prescribed point of the end – effector in a task space. There is a striking contrast between the apparent ease with which humans perform multijoint movements in the environment rich with obstacles, changing targets, and unpredictable forces, and the very modest progress in understanding how the central nervous system (CNS) controls such movements. The problem of redundancy is solved using sinergies which represent rules for relative

175 joint involvement to assure a desired endpoint trajectory. Term “ synergy” following means a set of rules that unite hypothetical control signals to individual joints into an equation helping to solve the problem of kinematic redundancy. Also, the possibility of switching synergies within a single movement according to task requirements may be an essential component of acquiring motor skill. In this paper it is proposed synergy approach to solve this problem. First, it is introduced generalized forces Q(t).Second, using local optimization of a suitable dynamic criterion in respect to ul , one can solved problem of redundancy with possibility of obtaining two synergy control in respect to ul within a single movement.