Approximate continuous-time optimal control in obstacle avoidance by time/space discretization of non-convex state constraints
Approximate continuous-time optimal control in obstacle avoidance by time/space discretization of non-convex state constraints
复制标题
通过非凸状态约束的时间/空间离散化避障的近似连续时间最优控制
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
H. Nijmeijer
中科院分区：
文献类型：
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作者：
H. L. Hagenaars;J. Imura;H. Nijmeijer
本文通过时间和空间的离散化处理了具有非凸状态约束的最优控制问题的一个近似版本，其中所追求的具体应用是避障问题。首先指出了标准的连续时间目标函数不适用于非凸状态约束下的最优控制问题，然后提出了一种新的包含中间目标状态的目标函数.接下来，对于具有该成本函数的最优控制问题，其中非凸状态约束关于时间轴和状态空间离散化，以显式形式给出最优连续时间控制，包括通过求解离散优化问题获得的中间目标状态。有效的算法，如广度优先搜索算法可以应用于这个离散的问题。因此，连续时间轨迹以及在每个离散时间的离散状态同时优化。最后，我们通过数值仿真说明了所提出的方法的有效性
This paper addresses an approximate version of the optimal control problem with non-convex state constraints via discretization of time and space, where the specific application pursued is the obstacle avoidance problem. First, it is pointed out that the standard continuous-time cost function with the final state fixed is not suitable to the optimal control problem under the non-convex state constraints, and then a new cost function including intermediate target states is proposed. Next, for the optimal control problem with this cost function, where the non-convex state constraints are discretized with respect to time axis and state space, an optimal continuous-time control is given in an explicit form, including the intermediate target states obtained by solving a discrete optimization problem. Efficient algorithms such as the breadth first search algorithm can be applied to this discrete problem. Thus the continuous-time trajectory as well as the discretized state at each discrete time is simultaneously optimized. Finally, we illustrate the effectiveness of the proposed approach with numerical simulations