Smooth Path Planning Using a Gaussian Process Regression Map for Mobile Robot Navigation

TL;DR

Problem: enable smooth, safe mobile robot navigation in unstructured environments by exploiting a continuous GPR map of obstacle distance and terrain traversability. Approach: gradient-descent Bézier curve optimisation (BCO) on a GPR map, with priors from A* or T-RRT to initialise control points, and a differentiable loss $L(B(t,P))$ balancing length, traversability, uncertainty, obstacle clearance, and curvature. Contributions: a complete GPR+BCO pipeline with prior-aware initialisation and a comparative evaluation showing priors improve convergence and path quality while maintaining constraints. Significance: supports online, smooth trajectory planning for ground robots in challenging terrains by integrating probabilistic environment representation with differentiable trajectory optimisation.

Abstract

In the context of ground robot navigation in unstructured hazardous environments, the coupling of efficient path planning with an adequate environment representation is a crucial topic in order to guarantee the robot safety while ensuring the accomplishment of its mission. This paper discusses the exploitation of an environment representation obtained via Gaussian process regression (GPR) for smooth path planning using gradient descent Bézier curve optimisation (BCO). A continuous differentiable GPR of the terrain traversability and obstacle distance is used to plan paths with a weighted A* discrete planner, a T-RRT sampling-based planner and BCO using A* or T-RRT computed paths as prior. Numerical experiments in procedurally generated 2D environments allowed to compare the paths planned by the described methods and highlight the benefits of the joint use of the GPR continuous representation and the BCO smooth path planning with these different priors.

Figures (4)

• Figure 1: Visualisation of a Gaussian process variational regression map over terrain traversability and obstacle distance from training data sampled in a randomly generated environment. Obstacles are displayed in black in the generated map image.
• Figure 2: Examples of paths computed by each evaluated method between random pairs of points in a procedurally generated GPR map. Colors represent the cumulative map related costs. Obstacles (i.e. coordinates at which $\bar{d}(x,y)\leq R)$ are displayed in black.
• Figure 3: Results of the comparison of the paths planned respectively by the A*, T-RRT, BCO-A*, BCO-RRT and BCO-$\O$. The A* and T-RRT prior computation times are respectively added to the BCO-A* and BCO-RRT optimisation times.
• Figure 4: Average over all generated paths of the total loss $L(B(t,P))$ and the different loss terms $L_o$, $L_c$, $L_T$, $L_\sigma$ and $L_l$ after each optimisation iteration for all experiments. Only 50 out of the maximum 500 iterations are displayed since all loss terms seem to have converged at this point.