This paper presents a method for motion planning under uncertainty to deal with situations where ambiguous data associations result in a multimodal hypothesis on the robot state. In the global localization problem, sometimes referred to as the "lost or kidnapped robot problem", given little to no a priori pose information, the localization algorithm should recover the correct pose of a mobile robot with respect to a global reference frame. We present a Receding Horizon approach, to plan actions that sequentially disambiguate a multimodal belief to achieve tight localization on the correct pose in finite time, i.e., converge to a unimodal belief. Experimental results are presented using a physical ground robot operating in an artificial maze-like environment. We demonstrate two runs wherein the robot is given no a priori information about its initial pose and the planner is tasked to localize the robot.
In the domain of global localization with a priori maps, @cite_24 showed that finding the optimal (shortest) plan to re-localize a kidnapped robot with multiple hypothesis in a deterministic setting (no sensing or motion uncertainty) is NP-hard. At best a greedy localization strategy can be developed whose plan length is upper bounded by @math , where @math is the number of hypothesis and @math is the length of the optimal plan. Compared to @cite_24 , we do not assume perfect sensing or actuation. In @cite_0 , the authors develop an active localization method in a grid based scheme for a known map. Their planning method considers arbitrary targets in the robot's local coordinate frame as atomic actions (e.g., move 1m right and 4m forward). The optimal action is selected based on the path cost and the expected decrease in entropy at the target. Compared to @cite_0 , our target selection methodology (Section and ) is active, i.e., M3P uses the a priori map information to select targets such that by visiting them, observation gap between belief modes is maximized resulting in successive disambiguation.
@cite_24 @cite_0
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We consider the problem of localizing a robot in a known environment modeled by a simple polygon P. We assume that the robot has a map of P but is placed at an unknown location inside P. From its initial location, the robot sees a set of points called the visibility polygon V of its location. In general, sensing at a single point will not suffice to uniquely localize the robot, since the set H of points in P with visibility polygon V may have more than one element. Hence, the robot must move around and use range sensing and a compass to determine its position (i.e., localize itself). We seek a strategy that minimizes the distance the robot travels to determine its exact location. We show that the problem of localizing a robot with minimum travel is NP-hard. We then give a polynomial time approximation scheme that causes the robot to travel a distance of at most (k - 1)d, where k = |H|, which is no greater than the number of reflex vertices of P, and d is the length of a minimum length tour that would allow the robot to verify its true initial location by sensing. We also show that this bound is the best possible. We have previously developed a mobile robot system which uses scale-invariant visual landmarks to localize and simultaneously build three-dimensional (3-D) maps of unmodified environments. In this paper, we examine global localization, where the robot localizes itself globally, without any prior location estimate. This is achieved by matching distinctive visual landmarks in the current frame to a database map. A Hough transform approach and a RANSAC approach for global localization are compared, showing that RANSAC is much more efficient for matching specific features, but much worse for matching nonspecific features. Moreover, robust global localization can be achieved by matching a small submap of the local region built from multiple frames. This submap alignment algorithm for global localization can be applied to map building, which can be regarded as alignment of multiple 3-D submaps. A global minimization procedure is carried out using the loop closure constraint to avoid the effects of slippage and drift accumulation. Landmark uncertainty is taken into account in the submap alignment and the global minimization process. Experiments show that global localization can be achieved accurately using the scale-invariant landmarks. Our approach of pairwise submap alignment with backward correction in a consistent manner produces a better global 3-D map. We propose an information-theoretic planning approach that enables mobile robots to autonomously construct dense 3D maps in a computationally efficient manner. Inspired by prior work, we accomplish this task by formulating an information-theoretic objective function based on CauchySchwarz quadratic mutual information (CSQMI) that guides robots to obtain measurements in uncertain regions of the map. We then contribute a two stage approach for active mapping. First, we generate a candidate set of trajectories using a combination of global planning and generation of local motion primitives. From this set, we choose a trajectory that maximizes the information-theoretic objective. Second, we employ a gradientbased trajectory optimization technique to locally refine the chosen trajectory such that the CSQMI objective is maximized while satisfying the robot’s motion constraints. We evaluated our approach through a series of simulations and experiments on a ground robot and an aerial robot mapping unknown 3D environments. Real-world experiments suggest our approach reduces the time to explore an environment by 70 compared to a closest frontier exploration strategy and 57 compared to an information-based strategy that uses global planning, while simulations demonstrate the approach extends to aerial robots with higher-dimensional state. We investigate the problem of planning under uncertainty, with application to mobile robotics. We propose a probabilistic framework in which the robot bases its decisions on the generalized belief, which is a probabilistic description of its own state and of external variables of interest. The approach naturally leads to a dual-layer architecture: an inner estimation layer, which performs inference to predict the outcome of possible decisions; and an outer decisional layer which is in charge of deciding the best action to undertake. Decision making is entrusted to a model predictive control MPC scheme. The formulation is valid for general cost functions and does not discretize the state or control space, enabling planning in continuous domain. Moreover, it allows to relax the assumption of maximum likelihood observations: predicted measurements are treated as random variables, and binary random variables are used to model the event that a measurement is actually taken by the robot. We successfully apply our approach to the problem of uncertainty-constrained exploration, in which the robot has to perform tasks in an unknown environment, while maintaining localization uncertainty within given bounds. We present an extensive numerical analysis of the proposed approach and compare it against related work. In practice, our planning approach produces smooth and natural trajectories and is able to impose soft upper bounds on the uncertainty. Finally, we exploit the results of this analysis to identify current limitations and show that the proposed framework can accommodate several desirable extensions.