Convex Receding Horizon Control in Non-Gaussian Belief Space
Convex Receding Horizon Control in Non-Gaussian Belief Space
复制标题
非高斯置信空间中的凸后退视界控制
DOI：
10.1007/978-3-642-36279-8_27
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Robert Platt
中科院分区：
文献类型：
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作者：
Robert Platt
解决部分可观察控制问题的主要挑战之一是在高维信念空间中进行规划。本质上，需要在参数空间中对状态空间上所有相关概率分布进行规划。文献探讨了不同的规划技术，包括轨迹优化[8,6]和路线图方法[12,4]。不幸的是，这些方法很难在后退的地平线控制环境中使用，因为可能需要在每个时间步重新规划。轨迹优化不能保证找到全局最优解，路线图方法的规划时间较长。本文给出了一个非平凡的凸性信念空间规划问题的实例，该实例可以快速且最优地求解高维问题。在温和的假设条件下，我们证明了所得到的控制策略最终会在信念空间中到达目标区域。由于凸信念空间规划问题的空间有一定的局限性，我们利用混合整数规划对该方法进行了扩展。我们建议提前求解问题的整数部分，这样在后退水平控制时只需要求解凸问题。
One of the main challenges in solving partially observable control problems is planning in high-dimensional belief spaces. Essentially, it is necessary to plan in the parameter space of all relevant probability distributions over the state space. The literature has explored different planning technologies including trajectory optimization [8, 6] and roadmap methods [12, 4]. Unfortunately, these methods are hard to use in a receding horizon control context where it is potentially necessary to replan on every time step. Trajectory optimization is not guaranteed to find globally optimal solutions and roadmap methods can have long planning times. This paper identifies a non-trivial instance of the belief space planning problem that is convex and can therefore be solved quickly and optimally even for high dimensional problems. We prove that the resulting control strategy will ultimately reach a goal region in belief space under mild assumptions. Since the space of convex belief space planning problem is somewhat limited, we extend the approach using mixed integer programming. We propose to solve the integer part of the problem in advance so that only convex problems need be solved during receding horizon control.