A hypothesis-based algorithm for planning and control in non-Gaussian belief spaces
We consider the partially observable control problem where it is potentially necessary to perform complex information-gathering operations in order to localize state. One approach to solving these problems is to create plans in belief-space, the space of probability distributions over the underlying state of the system. The belief-space plan encodes a strategy for performing a task while gaining information as necessary. Most approaches to belief-space planning rely upon representing belief state in a particular way (typically as a Gaussian). Unfortunately, this can lead to large errors between the assumed density representation and the true belief state. We propose a new computationally efficient algorithm for planning in non-Gaussian belief spaces. We propose a receding horizon re-planning approach where planning occurs in a low-dimensional sampled representation of belief state while the true belief state of the system is monitored using an arbitrary accurate high-dimensional representation. Our key contribution is a planning problem that, when solved optimally on each re-planning step, is guaranteed, under certain conditions, to enable the system to gain information. We prove that when these conditions are met, the algorithm converges with probability one. We characterize algorithm performance for different parameter settings in simulation and report results from a robot experiment that illustrates the application of the algorithm to robot grasping.
