Convex Receding Horizon Control in Non-Gaussian Belief Space

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. 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.