VCTP: Vehicle-Conditioned Terrain Planning for Off-Road Navigation

Kinodynamic planning for car-like vehicles on uneven terrain requires simultaneously optimizing competing objectives such as path efficiency and pose stability. This work presents an adaptive epsilon-constraint method integrated into a Model Predictive Control (MPC) framework, where the epsilon bounds are dynamically adjusted based on terrain descriptors to explore the Pareto front in real time. To capture vehicle-terrain dynamics, we develop a semi-parametric model combining analytical vehicle dynamics with a Sparse Gaussian Process (SGP) trained on the same terrain descriptors. The proposed epsilon-MPC is evaluated against MPPI and GAKD baselines, achieving a 94% navigation success rate while reducing maximum orientation deviation by 24% and improving multi-objective trade-off quality by 23%.

Real-time autonomous driving commonly relies on sampling-based trajectory planners that link candidate trajectories to target waypoints along the road centerline. The placement of these waypoints directly impacts both the existence and quality of feasible trajectories. Yet, its effect on planner performance remains largely unexplored. In this paper, we treat waypoint placement as a first-class design variable. We hold the trajectory primitive and candidate budget fixed, and systematically sweep three placement strategies (uniform spacing, an augmented Ramer-Douglas-Peucker variant (RDP*), and a novel curvature-conditioned allocation) across 449 configurations and five CommonRoad maps of increasing geometric complexity. Our results show that the nominal inter-waypoint spacing $d_s$ is the primary performance driver, with large differences in planner reliability attributed to placement alone. Uniform sampling at a well-tuned spacing matches or surpasses both RDP* and the centered curvature variant. The curvature variant offers a small but consistent advantage on geometrically complex roads under reliability-first and balanced weightings, while RDP* never outperforms uniform sampling. These findings suggest that $d_s$ should be treated as the dominant tuning parameter, with geometry-aware strategies reserved for curvature-rich corridors where feasibility is the limiting factor.

Simulation is crucial for developing and testing autonomous driving systems. In particular, the development of localization and control algorithms relies on an accurate vehicle dynamics simulation. However, most vehicle dynamics models are two-dimensional while real-world roads are three-dimensional. For example, effects from the three-dimensional road geometry on the Las Vegas Motor Speedway can increase the normal forces on the tires by more than 66% compared to the nominal load at standstill. As a result, even highly detailed planar vehicle dynamics models struggle to accurately reproduce the real vehicle's behavior. While solutions for three-dimensional vehicle dynamics exist, they are rarely adopted, computationally expensive, and complex. To address this issue, we present a novel method to couple planar vehicle dynamics models with real-world three-dimensional road geometry. We transform the planar vehicle state from the vehicle model's two-dimensional plane to its corresponding representation in three-dimensional space. Additionally, we calculate road-geometry-induced forces and moments and apply them to the planar vehicle model. We validate our approach using high-speed data recorded with a full-scale race car on the banked Las Vegas Motor Speedway. Furthermore, on synthetic tracks, we show that our method yields accurate results even in edge cases. Together, our results demonstrate that the gap between planar simulation and real-world three-dimensional roads can be closed without abandoning simpler planar models. To simplify adoption of our method, we provide the implementation as open-source software on github.com/TUMFTM/3d-road-geometry-coupling.