Bi-level Trajectory Optimization on Uneven Terrains with Differentiable Wheel-Terrain Interaction Model
arxiv(2024)
摘要
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.
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