A real-time approach for singularity avoidance in resolved motion rate control of robotic manipulators

Abstract

In autonomous system, it is important to establish a control scheme that works with stability even near singularity conJigurations. In this article, we describe an on-line trajectory control scheme that uses the manipulability measure as a distance criteria to avoid manipulator singularities.The proposed approach consists in a method for limiting the minimum value of the distance criteria. The pe$ormance is simply affected by the choice of the lower limit. Based on a real-time evaluation of the measure of manipulability, this method does not require a preliminary knowledge of the singular configurations. The proposed algorithm is validated by experimental results.

A supervisory loop approach to fulfill workspace constraints in redundant robots

“…In this case, (20) must be now changed to the "multiple-constraint" transversality condition of L g φ having full row rank, which indeed covers the previous single-constraint case (a one-row matrix is full rank if there exists a non-zero element).…”

“…Similar indexes of quadratic forms in the robot configuration q have been considered in the literature together with the robot manipulability [20] or the condition number of the Jacobian matrix [21] in order to avoid singular configurations. Furthermore, a performance index based on artificial potential fields [5] could also be considered to keep the robot away from the obstacles.…”

“…The necessary condition (20) for SM, which is known as the transversality condition [24], imposes that the sliding manifold must have unitary relative degree with respect to the discontinuous action, i.e., its first-order time derivative (φ i ) must explicitly depend on u. If this is not the case, an auxiliary subset Φ ⋄ ⊂ Φ which satisfies this condition should be properly defined [24].…”

“…Note that the last term of L f φ i depends on the disturbanceṗ d and b c . From the above definitions and assumptions, the values of α, K, ∇σ i and B are not zero 5 and, thus, the transversality condition (20) for only one active constraint is written as:…”

“…no solution of (24) exists, the robot motion must be stopped (i.e.q d must be set to zero) to avoid violating some constraint(s), giving rise to a blocking situation. For instance, such situation arises when the transversality condition (20) of an active constraint i is not satisfied and L f φ i > 0.…”