A Genetic Approach to Gradient-Free Kinodynamic Planning in Uneven Terrains

TL;DR

The paper addresses kinodynamic planning for car-like robots navigating uneven terrains represented as triangular meshes. It proposes GAKD, a gradient-free, GA-based planner that optimizes a fixed-horizon control sequence under a mesh-aware dynamic model, with a cost that trades distance to the goal against terrain traversability, and evaluates the approach against MPPI and log-MPPI in simulation and real-world tests. Results show GAKD reduces traversability cost by up to 20 percent while maintaining comparable path lengths, and demonstrates practical viability with ROS MBF integration and real-terrain experiments. This work advances gradient-free kinodynamic planning on complex terrains and suggests future improvements via annealing and data-driven dynamics.

Abstract

This paper proposes a genetic algorithm-based kinodynamic planning algorithm (GAKD) for car-like vehicles navigating uneven terrains modeled as triangular meshes. The algorithm's distinct feature is trajectory optimization over a fixed-length receding horizon using a genetic algorithm with heuristic-based mutation, ensuring the vehicle's controls remain within its valid operational range. By addressing challenges posed by uneven terrain meshes, such as changing face normals, GAKD offers a practical solution for path planning in complex environments. Comparative evaluations against Model Predictive Path Integral (MPPI) and log-MPPI methods show that GAKD achieves up to 20 percent improvement in traversability cost while maintaining comparable path length. These results demonstrate GAKD's potential in improving vehicle navigation on challenging terrains.

Figures (8)

• Figure 1: A radar chart comparing the performance of various motion planning methods across key criteria. While sampling-based approaches may lack global optimality, they are fast and practical, excelling in complex environments.
• Figure 2: Flow chart of the proposed genetic algorithm-based kinodynamic planning: GA is used to find the sequence of controls with the best fitness while ensuring all the controls in the sequence are from the space of valid controls.
• Figure 3: If a vehicle moves from $\mathbf{p_i}$ tangentially along face $\mathbf{F_1}$ to $\mathbf{p}_{i+1}^{\mathbf{f_1}}$, it has a tangential velocity $\mathbf{v}_{\text{tangent}}^{\mathbf{f}_1}$. Upon crossing into face $\mathbf{F_2}$, the next position is projected to $\mathbf{p}_{i+1}$ with a new tangential velocity $\mathbf{v}_{\text{tangent}}^{\mathbf{f}_2}$. The vehicle reference frame undergoes an orientation change from face $\mathbf{F_1}$ to face $\mathbf{F_2}$, with coordinates $({x}_1, {y}_1, {z}_1)$ on $\mathbf{F_1}$ transforming to $({x}_2, {y}_2, {z}_2)$ on $\mathbf{F_2}$.
• Figure 4: The blue arrows represent the face normals, while the dotted line represents the direction vector $\mathbf{j}$ from $\mathbf{P}$ to $\mathbf{P_{\text{target}}}$. In an ideal scenario where all faces are flat, the face normals along the path should be orthogonal to $\mathbf{j}$, the deviation from this which is penalized by $\Sigma$. For adjacent faces, if they are perfectly aligned, their normals should be parallel, and deviations from this are penalized by $\lambda$. The combination of $\Sigma$ and $\lambda$ defines $\Pi$, the traversability cost.
• Figure 6: Textured view of the uneven terrain mesh and some test scenarios.