A review of path following control strategies for autonomous robotic vehicles: theory, simulations, and experiments

TL;DR

This review analyzes path-following control for 2D autonomous vehicles by unifying PF methods under two main reference-frame approaches: path-frame stabilization and body-frame stabilization. It surveys seven PF methods ( Samson, Lapierre, LOS, Breivik, NMPC-based, Aguiar, and Alessandretti) and extends them to scenarios with disturbances and fully-actuated platforms, supported by theoretical Lyapunov proofs and stability guarantees. The work provides practical tools, including Matlab and Gazebo/ROS toolboxes, and validates PF strategies through simulations and field trials with Medusa marine vehicles, highlighting the importance of inner-outer loop time-scale separation and constraint-aware control. It also discusses the trade-offs between simple, robust PF designs and computationally intensive MPC/NMPC approaches, and points to future work in dynamics-aware PF and learning-based methods with stability guarantees.

Abstract

This article presents an in-depth review of the topic of path following for autonomous robotic vehicles, with a specific focus on vehicle motion in two dimensional space (2D). From a control system standpoint, path following can be formulated as the problem of stabilizing a path following error system that describes the dynamics of position and possibly orientation errors of a vehicle with respect to a path, with the errors defined in an appropriate reference frame. In spite of the large variety of path following methods described in the literature we show that, in principle, most of them can be categorized in two groups: stabilization of the path following error system expressed either in the vehicle's body frame or in a frame attached to a "reference point" moving along the path, such as a Frenet-Serret (F-S) frame or a Parallel Transport (P-T) frame. With this observation, we provide a unified formulation that is simple but general enough to cover many methods available in the literature. We then discuss the advantages and disadvantages of each method, comparing them from the design and implementation standpoint. We further show experimental results of the path following methods obtained from field trials testing with under-actuated and fully-actuated autonomous marine vehicles. In addition, we introduce open-source Matlab and Gazebo/ROS simulation toolboxes that are helpful in testing path following methods prior to their integration in the combined guidance, navigation, and control systems of autonomous vehicles.

Figures (32)

• Figure 2.1: Geometric illustration of the path following problem.
• Figure 2.2: Path following control systems; ${\bf u}_{\rm d}$: reference inputs (e.g. desired linear and angular speeds, orientations) for the autopilots; ${\bf p}$ and $\boldsymbol{\eta}$: the vehicle's position and orientation, respectively, ${\boldsymbol \tau}$: force and torque, $U_{\rm d}$: desired speed profile that the vehicle must track.
• Figure 2.3: Geometric illustration of the path following problem. $\{I\}, \{\mathcal{B}\}$, and $\{\mathcal{P}\}$ denote inertial/global, the vehicle body, and path frames, respectively. The symbols ${\bf p}$ and ${\bf p}_{\rm d}$ represent the position vectors of the vehicle and a generic point on the path, respectively expressed in $\{\mathcal{I}\}$.
• Figure 2.4: Under-actuated robotic vehicles
• Figure 2.5: Over-actuated robotic vehicles. Left: Fusion vehicle, produced by Strategic Robot Systems company equipped with the Guidance, Navigation, and Control systems developed by IST Lisbon; Right: M-Vector vehicle, developed by IST Lisbon. Notice in both vehicles the existence of 4 thrusters in the horizontal plane (2 at the bow and 2 at the stern, installed at slant angles), capable of imparting directly forces along the longitudinal and lateral axis and torque about the vertical axis.

Theorems & Definitions (25)

• Remark 1
• Remark 2
• Remark 3
• Theorem 3.1
• Remark 4
• Theorem 3.2
• Theorem 3.3
• Remark 5
• Remark 6
• Theorem 3.4