This paper explores the problem of path planning under uncertainty. Specifically, we consider online receding horizon based planners that need to operate in a latent environment where the latent information can be modeled via Gaussian Processes. Online path planning in latent environments is challenging since the robot needs to explore the environment to get a more accurate model of latent information for better planning later and also achieves the task as quick as possible. We propose UCB style algorithms that are popular in the bandit settings and show how those analyses can be adapted to the online robotic path planning problems. The proposed algorithm trades-off exploration and exploitation in near-optimal manner and has appealing no-regret properties. We demonstrate the efficacy of the framework on the application of aircraft flight path planning when the winds are partially observed.
: In receding-horizon control a library of pre-computed control command sequences are simulated forward from the current state of the robot using the dynamic motion model to come up with a set of dynamically feasible trajectories up to the planning horizon. This set of trajectories is then evaluated on the map of the world in the vicinity of the robot and amongst all the currently collision-free trajectories the one that makes most progress towards the goal is chosen for traversal @cite_5 . The selected trajectory is traversed for a portion of the time and the process of trajectory evaluation and selection is repeated again. Receding-horizon based planning has been widely used in aerial and ground robot navigation in cluttered environments @cite_4 @cite_18 @cite_21 due to many attractive properties like finite runtime, adaptability to available computational budget and dynamic feasibility by construction. We use receding-horizon planning with pre-computed trajectory libraries as the framework in this paper.
@cite_5 @cite_18 @cite_21 @cite_4
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There is extensive literature on using convex optimization to derive piece-wise polynomial trajectories for controlling differential flat systems with applications to three-dimensional flight for Micro Aerial Vehicles. In this work, we propose a method to formulate trajectory generation as a quadratic program (QP) using the concept of a Safe Flight Corridor (SFC). The SFC is a collection of convex overlapping polyhedra that models free space and provides a connected path from the robot to the goal position. We derive an efficient convex decomposition method that builds the SFC from a piece-wise linear skeleton obtained using a fast graph search technique. The SFC provides a set of linear inequality constraints in the QP allowing real-time motion planning. Because the range and field of view of the robot's sensors are limited, we develop a framework of Receding Horizon Planning , which plans trajectories within a finite footprint in the local map, continuously updating the trajectory through a re-planning process. The re-planning process takes between 50 to 300 ms for a large and cluttered map. We show the feasibility of our approach, its completeness and performance, with applications to high-speed flight in both simulated and physical experiments using quadrotors. We present a scalable robot motion planning algorithm for reach-avoid problems. We assume a discrete-time, linear model of the robot dynamics and a workspace described by a set of obstacles and a target region, where both the obstacles and the region are polyhedra. Our goal is to construct a trajectory, and the associated control strategy, that steers the robot from its initial point to the target while avoiding obstacles. Differently from previous approaches, based on the discretization of the continuous state space or uniform discretization of the workspace, our approach, inspired by the lazy satisfiability modulo theory paradigm, decomposes the planning problem into smaller subproblems, which can be efficiently solved using specialized solvers. At each iteration, we use a coarse, obstacle-based discretization of the workspace to obtain candidate high-level, discrete plans that solve a set of Boolean constraints, while completely abstracting the low-level continuous dynamics. The feasibility of the proposed plans is then checked via a convex program, under constraints on both the system dynamics and the control inputs, and new candidate plans are generated until a feasible one is found. To achieve scalability, we show how to generate succinct explanations for the infeasibility of a discrete plan by exploiting a relaxation of the convex program that allows detecting the earliest possible occurrence of an infeasible transition between workspace regions. Simulation results show that our algorithm favorably compares with state-of-the-art techniques and scales well for complex systems, including robot dynamics with up to 50 continuous states. This paper presents a novel path planning algorithm for autonomous, uncertainty-aware exploration and mapping of unknown environments using aerial robots. The proposed planner follows a two-step, receding horizon, belief space-based approach. At first, in an online computed tree the algorithm finds the branch that optimizes the amount of space expected to be explored. The first viewpoint configuration of this branch is selected, but the path towards it is decided through a second planning step. Within that, a new tree is sampled, admissible branches arriving at the reference viewpoint are found and the robot belief about its state and the tracked landmarks of the environment is propagated. The branch that minimizes the expected localization and mapping uncertainty is selected, the corresponding path is executed by the robot and the whole process is iteratively repeated. The proposed planner is capable of running online onboard a small aerial robot and its performance is evaluated using experimental studies in a challenging environment. This paper presents a strategy for planning robot motions in dynamic, uncertain environments (DUEs). Successful and efficient robot operation in such environments requires reasoning about the future evolution and uncertainties of the states of the moving agents and obstacles. A novel procedure to account for future information gathering (and the quality of that information) in the planning process is presented. To approximately solve the stochastic dynamic programming problem that is associated with DUE planning, we present a partially closed-loop receding horizon control algorithm whose solution integrates prediction, estimation, and planning while also accounting for chance constraints that arise from the uncertain locations of the robot and obstacles. Simulation results in simple static and dynamic scenarios illustrate the benefit of the algorithm over classical approaches. The approach is also applied to more complicated scenarios, including agents with complex, multimodal behaviors, basic robot-agent interaction, and agent information gathering.