提出带角约束流形，让机器人规划在复杂约束下仍能高效生成可行轨迹。
CMC-Opt: Constraint Manifold with Corners for Inequality-Constrained Optimization
- 用带角流形表示混合等式与不等式约束的可行状态空间
- 在大规模动力学规划中成功生成标准方法失败的可行轨迹
- 适合需要高鲁棒性约束优化的机器人运动规划场景
我们提出一种基于流形的框架，用于解决机器人领域常见的等式与不等式约束优化问题。该方法将原问题转化为直接在约束状态空间上的无约束优化问题。为此，我们引入“带角约束流形”来表示满足混合非线性等式与不等式约束的状态空间，并进一步扩展流形优化算法以适应这一新的拓扑结构。我们在大规模动力学规划任务中验证了该框架的强大与鲁棒性，成功生成了标准方法无法实现的动态可行轨迹。
原文摘要 · Abstract (English)
We introduce a manifold-based framework for addressing optimization problems with equality and inequality constraints found in robotics. Our approach transforms the original problem into an unconstrained optimization problem directly on the constrained state space. To achieve this, we introduce ``constraint manifolds with corners" to represent the state space satisfying mixed nonlinear equality and inequality constraints. We further extend manifold optimization algorithms to operate on this new topological structure. We demonstrate the power and robustness of our framework in the context of a large-scale kinodynamic planning problem, successfully generating dynamically feasible trajectories where standard methods fail.
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