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.
By contrast, the Adaptive Dimensionality (AD) approach, @cite_5 , explicitly decreases the dimensionality of the state-space in regions where full-dimensional planning is not needed. This approach introduces a strategy for adapting the dimensionality of the search space to guarantee a solution that is still feasible with respect to a high dimensional motion model while making fast progress in regions that exhibit only low-dimensional structure. In @cite_3 , path planning with adaptive dimensionality has been shown to be efficient for high-dimensional planning such as mobile manipulation. The AD approach has been extended in @cite_18 , to get faster planning times by introducing an incremental planning algorithm. @cite_10 extends this method in the context of mobile robots by using adaptively dimensional state-space to combine the global and local path planning problem for navigation. Our approach builds on the AD approach and applies it to path planning in dynamic environments.
@cite_5 @cite_18 @cite_10 @cite_3
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Path planning is often a high-dimensional computationally-expensive planning problem as it requires reasoning about the kinodynamic constraints of the robot and collisions of the robot with the environment. However, large regions of the environment are typically benign enough that a much faster low-dimensional planning combined with a local path following controller suffice. Planning with Adaptive Dimensionality that was recently developed makes use of this observation and iteratively constructs and searches a state-space consisting of mainly low-dimensional states. It only introduces regions of high-dimensional states into the state-space where they are necessary to ensure completeness and bounds on sub-optimality. However, due to its iterative nature, the approach relies on running a series of weighted A* searches. In this paper, we introduce and apply to Planning with Adaptive Dimensionality a simple but very effective incremental version of weighted A* that reuses its previously generated search tree if available. On the theoretical side, the new algorithm preserves guarantees on completeness and bounds on sub-optimality. On the experimental side, it speeds up 3D (x,y,heading) path planning with a full-body collision checking by up to a factor of 5. Our results also show that it tends to be much faster than applying alternative incremental graph search techniques such as D* to Planning with Adaptive Dimensionality. Path planning quickly becomes computationally hard as the dimensionality of the state-space increases. In this paper, we present a planning algorithm intended to speed up path planning for high-dimensional state-spaces such as robotic arms. The idea behind this work is that while planning in a high-dimensional state-space is often necessary to ensure the feasibilityof the resulting path, large portions of the path have a lower-dimensional structure. Based on this observation, our algorithm iteratively constructs a state-space of an adaptive dimensionality--a state-space that is high-dimensional only where the higher dimensionality is absolutely necessary for finding a feasible path. This often reduces drastically the size of the state-space, and as a result, the planning time and memory requirements. Analytically, we show that our method is complete and is guaranteed to find a solution if one exists, within a specified suboptimality bound. Experimentally, we apply the approach to 3D vehicle navigation (x, y, heading), and to a 7 DOF robotic arm on the Willow Garage’s PR2 robot. The results from our experiments suggest that ourmethod can be substantially faster than some of the state-of-the-art planning algorithms optimized for those tasks. Planning with kinodynamic constraints is often required for mobile robots operating in cluttered, complex environments. A common approach is to use a two-dimensional (2-D) global planner for long range planning, and a short range higher dimensional planner or controller capable of satisfying all of the constraints on motion. However, this approach is incomplete and can result in oscillations and the inability to find a path to the goal. In this paper we present an approach to solving this problem by combining the global and local path planning problem into a single search using a combined 2-D and higher dimensional state-space. Abstract Safe and efficient path planning for mobile robots in large dynamic environments is still a challenging research topic. In order to plan collision-free trajectories, the time component of the path must be explicitly considered during the search. Furthermore, a precise planning near obstacles and in the vicinity of the robot is important. This results in a high computational burden of the trajectory planning algorithms. However, in large open areas and in the far future of the path, the planning can be performed more coarsely. In this paper, we present a novel algorithm that uses a hybrid-dimensional multi-resolution state × time lattice to efficiently compute trajectories with an adaptive fidelity according to the environmental requirements. We show how to construct this lattice in a consistent way and define the transitions between regions of different granularity. Finally, we provide some experimental results, which prove the real-time capability of our approach and show its advantages over single-dimensional single-resolution approaches.