Path planning in the presence of dynamic obstacles is a challenging problem due to the added time dimension in search space. In approaches that ignore the time dimension and treat dynamic obstacles as static, frequent re-planning is unavoidable as the obstacles move, and their solutions are generally sub-optimal and can be incomplete. To achieve both optimality and completeness, it is necessary to consider the time dimension during planning. The notion of adaptive dimensionality has been successfully used in high-dimensional motion planning such as manipulation of robot arms, but has not been used in the context of path planning in dynamic environments. In this paper, we apply the idea of adaptive dimensionality to speed up path planning in dynamic environments for a robot with no assumptions on its dynamic model. Specifically, our approach considers the time dimension only in those regions of the environment where a potential collision may occur, and plans in a low-dimensional state-space elsewhere. We show that our approach is complete and is guaranteed to find a solution, if one exists, within a cost sub-optimality bound. We experimentally validate our method on the problem of 3D vehicle navigation (x, y, heading) in dynamic environments. Our results show that the presented approach achieves substantial speedups in planning time over 4D heuristic-based A*, especially when the resulting plan deviates significantly from the one suggested by the heuristic.
Some approaches only plan in full-dimensional space-time search space until the end of an obstacle's trajectory and then finish the plan in a low-dimensional state-space. Time-bounded lattice planning, @cite_2 , neglects dynamic obstacles and the time dimension in the search space after a certain point in the time. Several works, @cite_16 @cite_13 , have extended this algorithm to account for kinematic and dynamic feasibility in the resulting paths by using a hybrid dimensionality state-space. These approaches sacrifice optimality for faster planning times and don't provide theoretical guarantees on the sub-optimality of the solution. In addition, our algorithm doesn't prune the dynamic obstacle trajectories, instead takes the entire obstacle trajectories into account and returns a bounded sub-optimal collision-free path. Considering the entire trajectory of the obstacles ensures a globally optimal solution.
@cite_16 @cite_13 @cite_2
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In this work, we propose a search-based planning method to compute dynamically feasible trajectories for a quadrotor flying in an obstacle-cluttered environment. Our approach searches for smooth, minimum-time trajectories by exploring the map using a set of short-duration motion primitives. The primitives are generated by solving an optimal control problem and induce a finite lattice discretization on the state space which can be explored using a graph-search algorithm. The proposed approach is able to generate resolution-complete (i.e., optimal in the discretized space), safe, dynamically feasibility trajectories efficiently by exploiting the explicit solution of a Linear Quadratic Minimum Time problem. It does not assume a hovering initial condition and, hence, is suitable for fast online re-planning while the robot is moving. Quadrotor navigation with online re-planning is demonstrated using the proposed approach in simulation and physical experiments and comparisons with trajectory generation based on state-of-art quadratic programming are presented. In this paper we address the problem of motion planning in the presence of state uncertainty, also known as planning in belief space. The work is motivated by planning domains involving nontrivial dynamics, spatially varying measurement properties, and obstacle constraints. To make the problem tractable, we restrict the motion plan to a nominal trajectory stabilized with a linear estimator and controller. This allows us to predict distributions over future states given a candidate nominal trajectory. Using these distributions to ensure a bounded probability of collision, the algorithm incrementally constructs a graph of trajectories through state space, while efficiently searching over candidate paths through the graph at each iteration. This process results in a search tree in belief space that provably converges to the optimal path. We analyze the algorithm theoretically and also provide simulation results demonstrating its utility for balancing information gathering to reduce uncertainty and finding low cost paths. Safe navigation for mobile robots in unstructured and dynamic environments is still a challenging research topic. Most approaches use separate algorithms for global path planning and local obstacle avoidance. However, this generally results in globally sub-optimal navigation strategies. In this paper, we present an algorithm which combines these two navigation tasks in a single integrated approach. For this purpose, we introduce a novel search space, namely, a × lattice with hybrid dimensionality. We describe a procedure for generating high-quality motion primitives for a mobile robot with four-wheel steering to define the motion in this lattice. Our algorithm computes a hybrid solution for the path planning problem consisting of a trajectory (i.e., a path with time component) in the imminent future, a dynamically feasible path in the near future, and a kinematically feasible path for the remaining time to the goal. Finally, we provide some results of our algorithm in action to prove its high solution quality and real-time capability. We present an algorithm that produces a plan for relocating obstacles in order to grasp a target in clutter by a robotic manipulator without collisions. We consider configurations where objects are densely populated in a constrained and confined space. Thus, there exists no collision-free path for the manipulator without relocating obstacles. Since the problem of planning for object rearrangement has shown to be NP-hard, it is difficult to perform manipulation tasks efficiently which could frequently happen in service domains (e.g., taking out a target from a shelf or a fridge).Our proposed planner employs a collision avoidance scheme which has been widely used in mobile robot navigation. The planner determines an obstacle to be removed quickly in real time. It also can deal with dynamic changes in the configuration (e.g., changes in object poses). Our method is shown to be complete and runs in polynomial time. Experimental results in a realistic simulated environment show that our method improves up to 31 of the execution time compared to other competitors.