Distributed Motion Synchronisation Control of Humanoid Arms

A novel distributed adaptive control algorithm of a pair of humanoid robot arm system (Bristol-Elumotion-Robotic-Torso II (BERT II)) is proposed, analysed and simulated. Two humanoid arms are subjected to a distributed synchronisation control with a virtual leader-following trajectory to be followed, serving a potential application for a smooth cooperative task. The approach presented here is inspired by multi-agent theory. Graph theoretical concept such as Laplacian matrix is used to represent mutual communication between the two arms (regarded as agent nodes) with one of the arm `pinned' to a virtual leader (leader node). The stability of the proposed algorithm is analysed through Lyapunov technique. The algorithm features a sliding-mode term based adaptive law that captures directly the parameter estimation error. An auxiliary filtered regression vector and filtered computed torque is introduced. This allows the definition of another auxiliary matrix, a filtered regression matrix, which facilitates the introduction of the sliding term into the adaptation law. Parameter error convergence to zero can be guaranteed within finite-time with a Persistent-Excitation (PE) or Sufficient Richness condition for the virtual leader's trajectory.