Towards planning in generalized belief space

We investigate the problem of planning under uncertainty, which is of interest in several robotic applications, ranging from autonomous navigation to manipulation. Recent effort from the research community has been devoted to design planning approaches working in a continuous domain, relaxing the assumption that the controls belong to a finite set. In this case robot policy is computed from the current robot belief (planning in belief space), while the environment in which the robot moves is usually assumed to be known or partially known. We contribute to this branch of the literature by relaxing the assumption of known environment; for this purpose we introduce the concept of generalized belief space (GBS), in which the robot maintains a joint belief over its state and the state of the environment. We use GBS within a Model Predictive Control (MPC) scheme; our formulation is valid for general cost functions and incorporates a dual-layer optimization: the outer layer computes the best control action, while the inner layer computes the generalized belief given the action. The resulting approach does not require prior knowledge of the environment and does not assume maximum likelihood observations. We also present an application to a specific family of cost functions and we elucidate on the theoretical derivation with numerical examples.