Robust path following for autonomous vehicles with spatial PH quintic splines

TL;DR

This paper addresses robust path following for autonomous vehicles operating in disturbance-prone environments and potentially under-actuated configurations. It introduces a guidance framework built on tangent-continuous spatial $C^1$ PH quintic splines to generate smooth trajectories and a robust extended guidance law (EGL) that incorporates current disturbances, with an underlying current estimator. The approach is validated through comprehensive kinematic and dynamic simulations, including a 6-DoF Zeno AUV model with thrust limits, showing convergence to the path and accurate current estimation, plus efficient arc-length-based arrival-time computations via PH splines. The findings demonstrate that the proposed method preserves convergence under currents, improves robustness for under-actuated vehicles, and offers practical, computation-friendly trajectory timing suitable for real-time marine robotics applications.

Abstract

The distinctive feature of a polynomial parametric speed let polynomial Pythagorean-hodograph (PH) curves be attractive for the design of accurate and efficient application algorithms. We propose a robust path following scheme for the construction of smooth spatial motions by exploiting PH spline curves. In order to cover a general configuration setting, we present a guidance law which is suitable both for fully-actuated and (more common) under-actuated vehicles, which cannot control all the degrees of freedom. The robustness of the guidance law is enhanced by also taking into account the influence of wind or currents into the equations of motion. A selection of numerical experiments validates the effectiveness of the control strategy when $C^1$ spatial PH quintic interpolants are suitably considered for both kinematic and dynamic simulations.

Figures (6)

• Figure 1.2: Kinematic simulations: results obtained with the guidance law of Section \ref{['sec:03']} and \ref{['sec:04']} for the first simulation scenario. The path to be followed (solid line) is shown together with the path of the vehicle (dashed line) in a simulation without current (left) and with current when the basic guidance law (center) or its extension (right) are considered.
• Figure 1.3: Kinematic simulations: track errors obtained with the guidance laws of Section \ref{['sec:03']} (GL) and \ref{['sec:04']} (EGL) for the first simulation scenario. The results are shown for a simulation without current (left) and with current when the basic guidance law (center) or its extension (right) are considered.
• Figure 1.4: Kinematic simulations: results obtained considering the extended guidance laws of Section \ref{['sec:04']} for the last two scenarios. On the left (second scenario) and on the center (third scenario), the paths to be followed (solid line) are shown together with the paths of the vehicle (dashed line). The track errors obtained for the second (top) and third (bottom) simulation scenario are also shown (right).
• Figure 1.5: Kinematic simulations: estimation of the current velocity in the first (left), second (center), and third (right) simulation scenario.
• Figure 1.6: Dynamic simulations: the path to be followed (solid line) is shown together with the path of the vehicle (dashed line) for the first (left), the second (center), and the third (right) simulation scenario.