A LIE GROUP FORMULATION OF ROBOT DYNAMICS

In this article we present a unified geometric treatment of robot dyna mics. Using standard ideas from Lie groups and Riemannian geometry we formulate the equations of motion for an open chain manipulator both r ecursively and in closed form The recursive formulation leads to an O( n) algorithm that expresses the dynamics entirely in terms of coordina te-free Lie algebraic operations, The Lagrangian formulation also expr esses the dynamics in terms of these Lie algebraic operations and lead s to a particularly Simple set of closed-form equations, in which the kinematic and inertial parameters appear explicitly and independently of each other. The geometric approach permits a high-level, coordinate -free view of robot dynamics that skews explicitly some of the connect ions with the larger body of work bl mathematics and physics. At the s ame rime the resulting equations are shown to be computationally effec tive and easily differentiated and factored with respect to any of the robot parameters. This latter feature makes the ge ometric formulatio n attractive for applications such as robot design and calibration, mo tion optimization, and optimal control, where analytic gradients invol ving the dynamics are required.