Stability of Robotic Path Tracking. Part I: One-Dimensional Scalar Models

摘要

Stability of robotic path tracking can be violated because of different reasons. One of those is the time lag in the control system. Like in many other engineering problems, it is desirable to use the regimes of exploitation of robotic systems with near-critical values of control parameters. When crossing boundaries of stability domains (in the space of control parameters), the system can deviate from the desired regime either slightly or strongly. In the former case, the boundary of the stability domain is called safe, in the latter unsafe. When dealing with robotic systems working in the near-critical regimes, it is important to design relevant algorithms and control systems having safe boundaries only. In this report, the concept of safe boundaries of the stability domain is discussed regarding the time-lag driven destabilization of control systems. The first part of this report deals with the simplest models described by a single, first-order Ordinary Differential Equation with a retarded argument. More complex and sophisticated models will be analyzed in the forthcoming parts of the report. We demonstrate that when using currently popular Pure Pursuit algorithm of robot path tracking, the stability domain has unsafe boundary. The problem of the boundary safety can be handled by switching to another algorithm of path tracking, which we coined a "Hit-the-Road" algorithm.