Trajectory optimization on manifolds with applications to quadrotor systems
Trajectory optimization on manifolds with applications to quadrotor systems
复制标题
流形轨迹优化及其在四旋翼系统中的应用
DOI：
10.1177/0278364919891775
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Vijay R. Kumar
中科院分区：
文献类型：
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作者：
Michael Watterson;Sikang Liu;Ke Sun;Trey Smith;Vijay R. Kumar
流形在几乎所有的机器人应用中都被使用，即使它们没有被明确地建模。我们提出了一种微分几何方法来优化带有障碍的黎曼流形上的轨迹。优化问题取决于特定于流形的度量和碰撞函数。然后，我们提出了我们的流形上安全走廊(SCM)方法，该方法通过一个约束优化问题来计算优化机器人应用的轨迹。我们的方法不需要等式约束，这消除了在优化过程中投影回可行流形的需要。然后，我们演示了该算法如何在SO(3)上的一个示例问题上工作，以及一个视觉惯性导航机器人在三维导航中的感知规划示例。制定视场约束自然会导致使用流形R3×S 2建模，而不能将其建模为李群。我们还演示了在SE(3)上规划在充满障碍的环境中形成四旋翼飞行器的轨迹的例子。
Manifolds are used in almost all robotics applications even if they are not modeled explicitly. We propose a differential geometric approach for optimizing trajectories on a Riemannian manifold with obstacles. The optimization problem depends on a metric and collision function specific to a manifold. We then propose our safe corridor on manifolds (SCM) method of computationally optimizing trajectories for robotics applications via a constrained optimization problem. Our method does not need equality constraints, which eliminates the need to project back to a feasible manifold during optimization. We then demonstrate how this algorithm works on an example problem on SO ( 3 ) and a perception-aware planning example for visual–inertially guided robots navigating in three dimensions. Formulating field of view constraints naturally results in modeling with the manifold R 3 × S 2 , which cannot be modeled as a Lie group. We also demonstrate the example of planning trajectories on SE ( 3 ) for a formation of quadrotors within an obstacle filled environment.