Navigation of wheeled vehicles on uneven terrain necessitates going beyond the 2D approaches for trajectory planning. Specifically, it is essential to incorporate the full 6dof variation of vehicle pose and its associated stability cost in the planning process. To this end, most recent works aim to learn a neural network model to predict the vehicle evolution. However, such approaches are data-intensive and fraught with generalization issues. In this paper, we present a purely model-based approach that just requires the digital elevation information of the terrain. Specifically, we express the wheel-terrain interaction and 6dof pose prediction as a non-linear least squares (NLS) problem. As a result, trajectory planning can be viewed as a bi-level optimization. The inner optimization layer predicts the pose on the terrain along a given trajectory, while the outer layer deforms the trajectory itself to reduce the stability and kinematic costs of the pose. We improve the state-of-the-art in the following respects. First, we show that our NLS based pose prediction closely matches the output from a high-fidelity physics engine. This result coupled with the fact that we can query gradients of the NLS solver, makes our pose predictor, a differentiable wheel-terrain interaction model. We further leverage this differentiability to efficiently solve the proposed bi-level trajectory optimization problem. Finally, we perform extensive experiments, and comparison with a baseline to showcase the effectiveness of our approach in obtaining smooth, stable trajectories.

翻译：轮式车辆在不平坦地形上的导航需要超越二维轨迹规划方法，具体而言，必须在规划过程中纳入车辆完整六自由度位姿变化及其相关的稳定性代价。为此，近期大多数研究致力于学习神经网络模型以预测车辆状态演化。然而，此类方法数据需求大且泛化能力不足。本文提出一种纯模型驱动方法，仅需地形数字高程信息即可实现。具体而言，我们将轮地交互作用与六自由度位姿预测表述为非线性最小二乘问题。由此，轨迹规划可视为双层优化：内层优化层预测沿给定轨迹在地形上的位姿，外层优化层通过形变轨迹本身的代价，以降低位姿的稳定性与动力学代价。我们在以下方面实现了对现有技术的改进：首先，证明基于非线性最小二乘的位姿预测与高保真物理引擎的输出高度吻合。结合可查询非线性最小二乘求解器梯度的特性，使位姿预测器成为可微的轮地交互模型。进一步利用该可微性高效求解所提出的双层轨迹优化问题。最后，通过大量实验及与基准方法的对比，验证了本方法在获取平滑稳定轨迹方面的有效性。