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：摘要：轮式车辆在非平坦地形上的导航要求超越二维轨迹规划方法。具体而言，必须将车辆六自由度位姿变化及其相关稳定性代价纳入规划过程。为此，近期研究大多致力于学习预测车辆演化的神经网络模型，但这类方法数据需求量大且泛化能力不足。本文提出一种纯粹基于模型的方法，仅需地形数字高程信息即可实现规划。具体而言，我们将轮地交互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：内层优化层沿给定轨迹预测地形上的位姿，外层优化层则通过调整轨迹本身来降低位姿的稳定性代价和运动学代价。我们在以下方面改进了现有技术：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，我们的位姿预测器构成了可微的轮地交互模型。其次，利用该可微性高效求解所提双层轨迹优化问题。最终通过广泛实验及与基线方法的对比，验证了该方法在获取平滑稳定轨迹方面的有效性。