Fixed-Time Path-Following Control of an Autonomous Vehicle with Path-Dependent Performance and Feasibility Constraints

Constrained operations for autonomous vehicles have been extensively studied in the literature over the recent years. However, to the best of the authors' knowledge, all of the existing works address only constant or time-varying constraint functions. In this work, we study path-dependent constraint requirements, which explicitly depend on the path parameter, instead of depending on the time variable directly. This approach is more practical in reality, where the constraint requirements are often shaped by the environment boundaries. From the system users' perspectives, it is also much easier to define constraint functions based on the path parameter. A modified version of the universal barrier function is used in the analysis of path-dependent constraint requirements. We show that under the proposed novel control scheme, the vehicle's line-of-sight distance and angle error terms can converge into small sets near the equilibrium with a fixed-time convergence rate, while the path-dependent constraint requirements are satisfied at all time. A simulation and an experiment study further demonstrate the efficacy of the proposed scheme.