An alternative method to solving the kinematics of a redundant robot

The state occupied by an m degrees of freedom robot is determined by an articular joint position-vector q of R{sup m}, but usually the specification of a task by its task-vector X takes place in the operational space R{sup n}. Controlling the kinematics of a robot requires to find q as a function of X. In most of the cases, it is impossible to obtain this relationship analytically and globally. The problem is solved by linearization of the geometric model of the robot X = F(q) in the neighborhood of the point q, introducing the (n {times} m) Jacobian matrix: {Delta}X = J(q){Delta}q; {Delta}q {epsilon} R{sup m}; {Delta}X {epsilon} R{sup n}; where {Delta}X is the variation of task-vector, {Delta}q is the corresponding small variation of the articular position. 8 refs., 1 fig.