Wave-Based Analysis and Control of Lump-Modeled Flexible Robots

Flexible robots are frequently represented by lumped models. In the mechanics of lumped systems, wave concepts have been avoided, for good reasons, generally. In the control of lumped flexible systems, however, wave concepts prove very fruitful. This paper provides a foundation for the wave-based control application by exploring the validity and nature of wave concepts in lumped robotic systems. A new wave-based model of uniform mass-spring systems is proposed and verified. The model is exact but not unique. Useful simplifications and approximations are also presented. The model leads to control strategies for flexible robotic systems that are simple, powerful, robust, and generic. The wave approach also provides a new analysis tool and conceptual framework for lumped dynamic systems