Path planning using positive invariant sets
Path planning using positive invariant sets
复制标题
使用正不变集的路径规划
DOI：
10.1109/cdc.2016.7799188
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
S. D. Cairano
中科院分区：
文献类型：
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作者：
C. Danielson;A. Weiss;K. Berntorp;S. D. Cairano
我们提出一种算法，用于在满足输入约束和非凸输出约束的情况下，将线性系统的输出从一个可行的初始条件引导到期望的目标位置。系统输入由一组局部线性状态反馈控制器生成。路径规划算法使用图搜索来选择合适的局部控制器，其中图的节点是局部控制器，图的边表示在不违反输入或输出约束的情况下从一个局部控制器转换到另一个局部控制器的可能性。我们提出了两种计算局部控制器的方法。第一种方法使用固定增益控制器，并缩放其正不变集以满足输入和输出约束。我们提供了一个用于确定缩放因子的线性规划以及该线性规划具有闭式解的条件。第二种方法使用一个半定规划来设计局部控制器，该半定规划最大化满足状态和输入约束的正不变集的体积。我们在航天器对接上演示了我们的路径规划算法。基于半定规划的控制设计具有更好的性能，但需要更多的计算。
We present an algorithm for steering the output of a linear system from a feasible initial condition to a desired target position, while satisfying input constraints and nonconvex output constraints. The system input is generated by a collection of local linear state-feedback controllers. The path-planning algorithm selects the appropriate local controller using a graph search, where the nodes of the graph are the local controllers and the edges of the graph indicate when it is possible to transition from one local controller to another without violating input or output constraints. We present two methods for computing the local controllers. The first uses a fixed-gain controller and scales its positive invariant set to satisfy the input and output constraints. We provide a linear program for determining the scale-factor and a condition for when the linear program has a closed-form solution. The second method designs the local controllers using a semi-definite program that maximizes the volume of the positive invariant set that satisfies state and input constraints. We demonstrate our path-planning algorithm on docking of a spacecraft. The semi-definite programming based control design has better performance but requires more computation.