Kinematic Manipulability of Multi-joint Bio-inspired Extremities

Abstract

A linearised navigation control law for multi-legged walking robots is presented. The proposed model is stated in terms of robot's global acceleration, and formulated as an average of the Cartesian speeds of n-extremities of k-DOFs each. The state vector is defined as a general solution scoping three cases of robot's tangential acceleration: uniform, non-uniform, and constant speed. Leg's Cartesian velocities are described by their first order Jacobian, which results in redundant kinematics systems. As particular cases of study, two different biological kinematic configurations were analysed in order to be adapted (DOFs reductions) as potential kinematic functions of the navigation control law. Although, the research interest is centralised on walking systems, the Praying-Mantis raptorial legs, as well as the Smithi ant's legs are analysed. Because of the kinematic redundancy, by using pseudo-inverse numerical methods, the solution near a singularity region is unstable about these values. It was obtained the first-order derivative pseudo-inverse Jacobian matrix using two different numerical methods for multi-joint legs: the right pseudo-inverse, and by singularity properties using the singular value decomposition approach.