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In this paper, the redundancy resolution methods for elastic joint redundant robots are studied. First, a redundancy resolution method, called MD method is, proposed by using joint elastic deflection as a performance index. The influence of robots' initial configuration on this method is then discussed. Finally, simulations for a planar 3R redundant robot with elastic joints are conducted. Research results show that by optimizing robots' initial configuration this method can effectively reduce joint elastic deflection from a global point of view.