Stability Versus Maneuverability of Non-holonomic Differential Drive Mobile Robot: Focus on Aggressive Position Control Applications

This paper presents a novel control centric dynamic modeling analysis focused on the relationship between stability and maneuverability of non-holonomic differential drive robots. The impact of specific vehicle design parameters on stability, lateral and longitudinal maneuverability of robot are examined over a broad range of forward motion operating conditions. The central objective is to determine whether the directional instability created by placing the center of gravity (c.g.) behind wheel-axle, aids in the performance of a robot executing aggressive cornering maneuvers. To this end, the paper explores two outer-loop position control applications, (1) Trajectory tracking using Lyapunov based method, (2) Minimum-time maneuvering of racetrack using Model Predictive Control (MPC) strategy. A hierarchical inner-outer loop control architecture with a weighted $\mathcal{H}^{\infty}$ mixed sensitivity based inner-loop velocity tracking system, is presented for the same. The advantages and disadvantages of proposed modeling approach and associated control relevant performance tradeoffs are demonstrated through simulations in discrete time.