Velocity and Acceleration Cones for Kinematic and Dynamic Constraints on Omni-Directional Mobile Robots

We consider the problems of kinematic and dynamic constraints, with actuator saturation and wheel slippage avoidance, for motion planning of a holonomic three-wheeled omni-directional robot. That is, the motion planner must not demand more velocity and acceleration at each time instant than the robot can provide. A new coupled non-linear dynamics model is derived. The novel concepts of Velocity and Acceleration Cones are proposed for determining the kinematic and dynamic constraints. The Velocity Cone is based on kinematics; we propose two Acceleration Cones, one for avoiding actuator saturation and the other for avoiding wheel slippage. The wheel slippage Acceleration Cone was found to dominate. In practical motion, all commanded velocities and accelerations from the motion planner must lie within these cones for successful motion. Case studies, simulations, and experimental validations are presented for our dynamic model and controller, plus the Velocity and Acceleration Cones.