Hierarchical constraint-based singularity avoidance

A reflexive approach for the hierarchical constraint-based singularity avoidance is proposed and demonstrated on the example of a two-link planar robot. The method is based on the concept of lower level constraint adaptation by introducing virtual velocity constraints in relation to higher level system states and on the concept of anisotropic reflexive trajectory deflection. Constraints adaptation utilizes a metaphor of virtual damping the end effector in task space. Clipping errors in joint space are transferred to the task space using the robot´s Jacobi matrix and a deviation parameter-matrix. Thus the position and velocity control behavior in the vicinity of a singular configuration is influenced in a way that this singularity can be safely avoided and constraints in the task and joint space can be hold. Furthermore, redundant degrees of freedom can be used to minimize the position error reflexively without calculating new trajectories.