Languages, Behaviors, Hybrid Architectures, and Motion Control

Abstract

In this paper we put forward a framework that integrates features of reactive planning models with modern control-theory-based approaches to motion control of robots. We introduce a motion description language, MDLe, inspired by Roger Brockett’s MDL, that provides a formal basis for robot programming using behaviors, and at the same time permits incorporation of kinematic and dynamic models of robots given in the form of differential equations. In particular, behaviors for robots are formalized in terms of kinetic state machines, a motion description language, and the interaction of the kinetic state machine with realtime information from (limited range) sensors. This formalization allows us to create a mathematical basis for the study of such systems, including techniques for integrating sets of behaviors. In addition we suggest cost functions for comparing both atomic and compound behaviors in various environments. We demonstrate the use of MDLe in the area of motion planning for nonholonomic robots. Such models impose limitations on stabilizability via smooth feedback; piecing together open-loop and closed-loop trajectories becomes essential in these circumstances, and MDLe enables one to describe such piecing together in a systematic manner. A reactive planner using the formalism of this discussion is described. We demonstrate obstacle avoidance with limited range sensors as a test of this planner.