Centroidal Momentum Matrix of a humanoid robot: Structure and properties

— The centroidal momentum of a humanoid robot is the sum of the individual link momenta, after projecting each to the robot’s Center of Mass (CoM). Centroidal momentum is a linear function of the robot’s generalized velocities and the Centroidal Momentum Matrix is the matrix form of this function. This matrix has been called both a Jacobian matrix and an inertia matrix by others. We show that it is actually a product of a Jacobian and an inertia matrix. We establish the relationship between the Centroidal Momentum Matrix and the well-known joint-space inertia matrix. We present a Transformation Diagram that graphically captures the inter-relationships of the matrix operators and motion and momentum variables in Joint Space, CoM Space as well as the System Space. The Centroidal Momentum Matrix is a local scaling function that maps the joint rates to the centroidal momentum. Following the concept of the manipulability ellipsoid, we propose the centroidal momentum ellipsoid that qua...

• Type: Conference
• Year: 2008
• Where: IROS
• Authors: David E. Orin, Ambarish Goswami
• Keywords: Centroidal Momentum, Centroidal Momentum Matrix, Inertia Matrix, IROS 2008, Robotics