Bounds on robot dynamics

The authors develop simple configuration-independent bounds on the dynamics of a robot manipulator. In particular, the inertia and gravity tensors and their derivatives of all orders for open-kinematic-chain manipulators. The bounds are useful in dynamics interpolation bounding the Coriolis and centrifugal forces (since these depend on the derivatives of the inertia tensor), suboptimal control, and path planning with dynamical constraints. These bounds can be used for verifying that trajectories satisfy actuator constraints. The bounds on the derivatives of the inertia tensor bound Coriolis and centrifugal forces and determine whether or not they can be ignored along a trajectory. The bounds on the derivatives also permit reliable interpolation of feedforward terms of dynamic compensation in control. In addition, they may also be used to simplify convergence proofs in nonlinear control schemes where detailed estimates of the dynamics are required, and they are useful in a variety of planning and optimization problems to prove the correctness of algorithms