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In this paper, we address the problem of stochastic motion planning under partial observability, more specifically, how to navigate a mobile robot equipped with continuous range sensors such as LIDAR. In contrast to many existing robotic motion planning methods, we explicitly consider the uncertainty of the robot state by modeling the system as a POMDP. Recent work on general purpose POMDP solvers is typically limited to discrete observation spaces, and does not readily apply to the proposed problem due to the continuous measurements from LIDAR. In this work, we build upon an existing Monte Carlo Tree Search method, POMCP, and propose a new algorithm POMCP++. Our algorithm can handle continuous observation spaces with a novel measurement selection strategy. The POMCP++ algorithm overcomes over-optimism in the value estimation of a rollout policy by removing the implicit perfect state assumption at the rollout phase. We validate POMCP++ in theory by proving it is a Monte Carlo Tree Search algorithm. Through comparisons with other methods that can also be applied to the proposed problem, we show that POMCP++ yields significantly higher success rate and total reward.
In this work, we use iterative Linear Quadratic Gaussian (iLQG) to plan motions for a mobile robot with range sensors in belief space. We address two limitations that prevent applications of iLQG to the considered robotic system. First, iLQG assumes a differentiable measurement model, which is not true for range sensors. We show that iLQG only requires the differentiability of the belief dynamics. We propose to use a derivative-free filter to approximate the belief dynamics, which does not require explicit differentiability of the measurement model. Second, informative measurements from a range sensor are sparse. Uninformative measurements produce trivial gradient information, which prevent iLQG optimization from converging to a local minimum. We densify the informative measurements by introducing additional parameters in the measurement model. The parameters are iteratively updated in the optimization to ensure convergence to the true measurement model of a range sensor. We show the effectiveness of the proposed modifications through an ablation study. We also apply the proposed method in simulations of large scale real world environments, which show superior performance comparing to the state-of-the-art methods that either assume the separation principle or maximum likelihood measurements.
Planning smooth and energy-efficient motions for wheeled mobile robots is a central task for applications ranging from autonomous driving to service and intralogistic robotics. Over the past decades, a wide variety of motion planners, steer functions and path-improvement techniques have been proposed for such non-holonomic systems. With the objective of comparing this large assortment of state-of-the-art motion-planning techniques, we introduce a novel open-source motion-planning benchmark for wheeled mobile robots, whose scenarios resemble real-world applications (such as navigating warehouses, moving in cluttered cities or parking), and propose metrics for planning efficiency and path quality. Our benchmark is easy to use and extend, and thus allows practitioners and researchers to evaluate new motion-planning algorithms, scenarios and metrics easily. We use our benchmark to highlight the strengths and weaknesses of several common state-of-the-art motion planners and provide recommendations on when they should be used.
We study the problem of synthesizing a controller that maximizes the entropy of a partially observable Markov decision process (POMDP) subject to a constraint on the expected total reward. Such a controller minimizes the predictability of a decision-makers trajectories while guaranteeing the completion of a task expressed by a reward function. First, we prove that a decision-maker with perfect observations can randomize its paths at least as well as a decision-maker with partial observations. Then, focusing on finite-state controllers, we recast the entropy maximization problem as a so-called parameter synthesis problem for a parametric Markov chain (pMC). We show that the maximum entropy of a POMDP is lower bounded by the maximum entropy of this pMC. Finally, we present an algorithm, based on a nonlinear optimization problem, to synthesize an FSC that locally maximizes the entropy of a POMDP over FSCs with the same number of memory states. In numerical examples, we demonstrate the proposed algorithm on motion planning scenarios.
Control and communication are often tightly coupled in motion planning of networked mobile robots, due to the fact that robotic motions will affect the overall communication quality, and the quality of service (QoS) of the communication among the robots will in turn affect their coordination performance. In this paper, we propose a control theoretical motion planning framework for a team of networked mobile robots in order to accomplish high-level spatial and temporal motion objectives while optimizing communication QoS. Desired motion specifications are formulated as Signal Temporal Logic (STL), whereas the communication performances to be optimized are captured by recently proposed Spatial Temporal Reach and Escape Logic (STREL) formulas. Both the STL and STREL specifications are encoded as mixed integer linear constraints posed on the system and/or environment state variables of the mobile robot network, where satisfactory control strategies can be computed by exploiting a distributed model predictive control (MPC) approach. To the best of the authors knowledge, we are the first to study controller synthesis for STREL specifications. A two-layer hierarchical MPC procedure is proposed to efficiently solve the problem, whose soundness and completeness are formally ensured. The effectiveness of the proposed framework is validated by simulation examples.
For heterogeneous unmanned systems composed of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs), using UAVs serve as eyes to assist UGVs in motion planning is a promising research direction due to the UAVs vast view scope. However, due to UAVs flight altitude limitations, it may be impossible to observe the global map, and motion planning in the local map is a POMDP (Partially Observable Markov Decision Process) problem. This paper proposes a motion planning algorithm for heterogeneous unmanned system under partial observation from UAV without reconstruction of global maps, which consists of two parts designed for perception and decision-making, respectively. For the perception part, we propose the Grid Map Generation Network (GMGN), which is used to perceive scenes from UAVs perspective and classify the pathways and obstacles. For the decision-making part, we propose the Motion Command Generation Network (MCGN). Due to the addition of memory mechanism, MCGN has planning and reasoning abilities under partial observation from UAVs. We evaluate our proposed algorithm by comparing with baseline algorithms. The results show that our method effectively plans the motion of heterogeneous unmanned systems and achieves a relatively high success rate.