Model Predictive Path-Following Framework for Generalized N-Trailer Vehicles in the Presence of Dynamic Obstacles Modeled as Soft Constraints

Abstract

Collision avoidance is crucial for autonomous navigation systems. Many studies have addressed obstacle avoidance for single unicycles and car-like vehicles in on-road conditions. In this work, we extend the scope to generalised N-trailer vehicles, comprising a single active segment pulling multiple trailers. Unlike approaches that treat obstacles as hard constraints, we model them as soft constraints using Gaussian functions. This method maintains the convexity of the search space, reducing computational demands. However, the regions occupied by obstacles remain feasible. Thus, the Gaussian function’s amplitudes need to be carefully chosen to discourage navigation through these areas. Moreover, closed-loop stability is guaranteed by generating auxiliary references when the nominal path is occluded. The efficacy of this approach is demonstrated through simulated and field experiments with a tractor pulling two trailers. These experiments show the method’s capability to navigate around obstacles efficiently while maintaining computational efficiency, validating its practical applicability. Videos of the experiments and the implemented algorithms are available at https://usmcl-my.sharepoint.com/:f:/g/personal/nestor_deniz_usm_cl/EtU54g1NeslNhD8V7dAeu20B0umnQa4FKiMlzThkTAXYvg?e=swEXwg. Despite the success in real-time implementation, more research is needed to address the open questions discussed at the end of this article. Note to Practitioners—This work focuses on implementing obstacle avoidance for a kind of vehicles widely used in agriculture, mining, luggage transportation, and industry. A LiDAR Velodyne VLP16, configured with its lowest rotation speed for denser point clouds, is used to scan the environment. Proper attachment of the LiDAR to the tractor’s body minimises vibration and azimuth movements, ensuring accurate obstacle detection. Obstacles are modelled as Gaussian functions to maintain the convexity and optimise computational efficiency. The Gaussian function’s amplitude should be set high enough to effectively avoid collision when density of obstacle is high. The framework uses a control horizon $N_{c}$ and a prediction horizon $N_{p}$ beyond the control to anticipate obstacle’s position. However, a large prediction horizons $N_{p}$ is not advised when the model of the dynamic of the obstacles is not accurate.