Motion planning of the multi-bar system: The imbalanced jacobian algorithm

Abstract

We study the motion planning problem for the multi-bar system composed of a series of rigid bars connected by spherical joints, moving in R3 and subject to non-holonomic constraints. The control system representation of the system takes the form of a driftless control system with 3 inputs. In order to avoid representation singularities, the constrained motion planning problem is addressed and solved using the imbalanced Jacobian algorithm. Performance of the algorithm is illustrated with the example of the 2-bar system.