Global Motion Planning under Uncertain Motion, Sensing, and Environment Map

Motion planning that takes into account uncertainty in motion, sensing, and environment map, is critical for autonomous robots to operate reliably in our living spaces. Partially Observable Markov Decision Processes (POMDPs) is a principled and general framework for planning under uncertainty. Although recent development of point-based POMDPs have drastically increased the speed of POMDP planning, even the best POMDP planner today, fails to generate reasonable motion strategies when the environment map is not known exactly. This paper presents Guided Cluster Sampling (GCS), a new point-based POMDP planner for motion planning under uncertain motion, sensing, and environment map, when the robot has active sensing capability. It uses our observations that in this problem, the belief space B can be partitioned into a collection of much smaller subspaces, and an optimal policy can often be generated by sufficient sampling of a small subset of the collection. GCS samples B using two-stage cluster sampling, a subspace is sampled from the collection and then a belief is sampled from the subspace. It uses information from the set of sampled sub-spaces and sampled beliefs to guide subsequent sampling. Preliminary results suggest that GCS generates reasonable policies for motion planning problems with uncertain motion, sensing, and environment map, that are unsolvable by the best point-based POMDP planner today, within reasonable time. Furthermore, GCS handles POMDPs with continuous state, action, and observation spaces. We show that for a class of POMDPs that often occur in robot motion planning, GCS converges to the optimal policy, given enough time. To the best of our knowledge, this is the first convergence result for point-based POMDPs with continuous action space

A Bayesian framework for optimal motion planning with uncertainty

Modeling robot motion planning with uncertainty in a Bayesian framework leads to a computationally intractable stochastic control problem. We seek hypotheses that can justify a separate implementation of control, localization and planning. In the end, we reduce the stochastic control problem to path- planning in the extended space of poses x covariances; the transitions between states are modeled through the use of the Fisher information matrix. In this framework, we consider two problems: minimizing the execution time, and minimizing the final covariance, with an upper bound on the execution time. Two correct and complete algorithms are presented. The first is the direct extension of classical graph-search algorithms in the extended space. The second one is a back-projection algorithm: uncertainty constraints are propagated backward from the goal towards the start state

Informative Path Planning for Active Field Mapping under Localization Uncertainty

Information gathering algorithms play a key role in unlocking the potential of robots for efficient data collection in a wide range of applications. However, most existing strategies neglect the fundamental problem of the robot pose uncertainty, which is an implicit requirement for creating robust, high-quality maps. To address this issue, we introduce an informative planning framework for active mapping that explicitly accounts for the pose uncertainty in both the mapping and planning tasks. Our strategy exploits a Gaussian Process (GP) model to capture a target environmental field given the uncertainty on its inputs. For planning, we formulate a new utility function that couples the localization and field mapping objectives in GP-based mapping scenarios in a principled way, without relying on any manually tuned parameters. Extensive simulations show that our approach outperforms existing strategies, with reductions in mean pose uncertainty and map error. We also present a proof of concept in an indoor temperature mapping scenario.Comment: 8 pages, 7 figures, submission (revised) to Robotics & Automation Letters (and IEEE International Conference on Robotics and Automation