Belief space planning assuming maximum likelihood observations

By Robert Platt Jr., Russ Tedrake, Leslie Pack Kaelbling, Tomas Lozano-Perez. Robotics: Science and Systems Conference, 2010

423 citations recorded by the source corpus.

We cast the partially observable control problem as a fully observable underactuated stochastic control problem in belief space and apply standard planning and control techniques. One of the difficulties of belief space planning is modeling the stochastic dynamics resulting from unknown future observations. The core of our proposal is to define deterministic beliefsystem dynamics based on an assumption that the maximum likelihood observation (calculated just prior to the observation) is always obtained. The stochastic effects of future observations are modeled as Gaussian noise. Given this model of the dynamics, two planning and control methods are applied. In the first, linear quadratic regulation (LQR) is applied to generate policies in the belief space. This approach is shown to be optimal for linearGaussian systems. In the second, a planner is used to find locally optimal plans in the belief space. We propose a replanning approach that is shown to converge to the belief space goal in a finite number of replanning steps. These approaches are characterized in the context of a simple nonlinear manipulation problem where a planar robot simultaneously locates and grasps an object.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/3a13bb6e950dc39d62f816ac1584b68215b0d815

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Citations in the corpus

Integrated task and motion planning in belief space (2013, background): “Recent research (du Toit and Burdick, 2010; Erez and Smart, 2010; Hauser, 2010; Platt et al., 2010) has established the value of control in belief space using simplified models and replanning.”
LQG-MP: Optimized path planning for robots with motion uncertainty and imperfect state information (2010, background): “Existing planners that are most directly related to LQG-MP take into account the available sensing capability to maximize the probability of arriving at the goal or to minimize expected cost [9, 12, 26, 27, 29].”
A Review of Robot Learning for Manipulation: Challenges, Representations, and Algorithms (2019, methodology): “LQR-like methods also assume that the state is fully observable; Linear Quadratic Gaussian (LQG) control methods further generalize LQR by using a Kalman filter for state estimation, in conjunction with an LQR controller [239, 303].”
Online Replanning in Belief Space for Partially Observable Task and Motion Problems (2019, methodology): “When applied to observation actions, this approach is called maximum likelihood observation (MLO) determinization [23], [24], [15].”
A Survey on Active Simultaneous Localization and Mapping: State of the Art and New Frontiers (2022, methodology): “Index Terms—Active perception, active simultaneous localization and mapping (SLAM), autonomous robotic exploration, belief-space planning (BSP), deep reinforcement learning (DRL), next best view, optimality criteria.”
Rapidly-exploring Random Belief Trees for motion planning under uncertainty (2011, background): “While Σt captures the uncertainty that will be present on-line during path execution, it does not represent the full uncertainty from a planning perspective since the mean of the state estimate, x̂t, will not lie on the nominal trajectory as assumed in [11], [12], [18], [19] and others.”