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The paper presents a new solution of inverse displacement analysis of the general six degree-of-freedom serial robot.The inverse displacement analysis of the general serial robot is transformed into a minimization problem and then the optimization method is adopted to solve the nonlinear least squares problem with the analytic form of new Jacobian matrix.In this way,joint variables of the general serial robot can be searched out quickly under the desired precision when positions of the three non-collinear end effector points are given.Compared with the general Newton iterative method,the proposed algorithm can search out the solution when the robot is at the singular configuration and the initial configuration used in the optimization method may also be the singular configuration.So the convergence domain is bigger than that of the general Newton iterative method.Another advantage of the proposed algorithm is that positions of the three non-collinear end effector points are usually much easier to be measured than the orientation of the end effector.The inverse displacement analysis of the general 6R(six-revolute-joint) serial robot is illustrated as an example and the simulation results verify the efficiency of the proposed algorithm.Because the three non-collinear points can be selected at random,the method can be applied to any other types of serial robots.
The paper presents a new solution of inverse displacement analysis of the general six degree-of-freedom serial robot. The inverse displacement analysis of the general serial robot is transformed into a minimization problem and then the optimization method is solved to the nonlinear least squares problem with the analytic form of new Jacobian matrix. In this way, joint variables of the general serial robot can be searched out quickly under the desired precision when positions of the three non-collinear end effector points are given. Compared with the general Newton iterative method, the proposed algorithm can search out the solution when the robot is at the singular configuration and the initial configuration used in the optimization method may also be the singular configuration. so the convergence domain is bigger than that of the general Newton iterative method. Another advantage of the proposed algorithm is that positions of the three non-collinear end effector points are usually muc h easier to be measured than the orientation of the end effector. the inverse displacement analysis of the general 6R (six-revolute-joint) serial robot is illustrated as an example and the simulation results verify the efficiency of the proposed algorithm.Because the three non-collinear points can be selected at random, the method can be applied to any other types of serial robots.