Continuous path planning with multiple constraints
Continuous path planning with multiple constraints
复制标题
具有多重约束的连续路径规划
DOI：
10.1109/cdc.2003.1272513
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
S. Sastry
中科院分区：
文献类型：
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作者：
Ian M. Mitchell;S. Sastry
我们研究了一个低维连续状态空间的路径规划问题，该空间受几个附加代价度量的上界约束。对于单代价情况，先前发表的研究已经提出通过局部最小自由值函数的梯度下降来构建路径。该值函数是Eikonal偏微分方程的解，并设计了有效的算法来计算它。在本文中，我们提出了一个辅助偏微分方程，我们可以用它来评估由值函数产生的路径的多个附加成本指标；求解这个辅助方程给值函数的计算增加了一点工作量。然后，我们提出了一种算法，该算法为每个可能的目的地生成代价位于帕累托最优曲面上的路径，我们可以从这些路径中选择满足约束的路径。当状态空间维度和成本指标数量的总和大致为6或更低时，该过程是实用的。
We examine the problem of planning a path through a low dimensional continuous state space subject to upper bounds on several additive cost metrics. For the single cost case, previously published research has proposed constructing the paths by gradient descent on a local minima free value function. This value function is the solution of the Eikonal partial differential equation, and efficient algorithms have been designed to compute it. In this paper we propose an auxiliary partial differential equation with which we can evaluate multiple additive cost metrics for paths which are generated by value functions; solving this auxiliary equation adds little more work to the value function computation. We then propose an algorithm which generates paths whose costs lie on the Pareto optimal surface for each possible destination location, and we can choose from these paths those which satisfy the constraints. The procedure is practical when the sum of the state space dimension and number of cost metrics is roughly six or below.