Evaluation and Time-Scaling of Trajectories for Wheeled Mobile Robots

We present a method for evaluating the feasibility of trajectories generated by path-planing systems for wheeled mobile robots (WMRs). Constraints that limit the class of executable trajectories for a given WMR are classified as path constraints, kinematic constraints, and dynamic constraints. Path constraints, which are limits on the path geometry, are a function of the wheelbase configuration and steering mechanism. Limits that involve only functions of velocities and accelerations are termed kinematic constraints. Dynamic constraints refer to limits on force/torque inputs and frictional force constraints which must be satisfied for a trajectory to be feasible. We show that when path constraints are violated the path must be modified to achieve feasibility, while violations of kinematic and dynamic constraints can be eliminated by time scaling so that the same path is followed at a slower speed. The concepts are developed and illustrated in the context of a model for the dynamics of a conventionally steered vehicle.