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We proposed a new approach for redundant robots trajectories planning, based on the Null space (or Kernel) features. The Null space (Kernel) exists only in the case of redundant robots and it describes these joints motion which do not affect the robot end-effector motion in the sense of both position and orientation. Based on this “hidden motion” realized in the configuration space, which does not affect the motion in the working zone, we can control independently the robot end-effector position and orientation motions, or just maintain its state while some external force is applied to it. The proposed control strategy is simple, no additional penalty functions are used to restraint the end-effector motion as in the case of the conventional methods. No pseudo inverse kinematics calculations are required; the desired trajectories are generated directly in the configuration space. No complicated control schemes are introduced, the proposed method is based on solving algebraic systems of equations and finding eigenvectors and eigenvalues. In the paper the results from simulations and experiments based on the proposed method are presented and discussed.

This work is dedicated to accuracy control of redundant robot-manipulators using sensibility approach. A manifold structure is applied to realize bases transition at local robot level. This assures optimal choice of drive subsets or combination of drives realizing motion with desired sensibility. The formulated condition satisfaction in the robot configurational space leads to precise trajectory tracing in the working zone (coincidence of the sensibility direction with the trajectory tangent vector). An illustrative example is presented and the explicit results are shown. The group theory application completes the considerations and it is helpful for better mechanical interpretation.

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