Space Adaptive Search for Nonholonomic Mobile Robots Path Planning

TL;DR

The paper addresses nonholonomic mobile robot path planning by introducing Space Adaptive Search (SAS), which operates in a discrete 3D state-space $S^3=\{x, y, \theta\}$ and updates an adaptive neighborhood rather than only the current state. SAS defines an effective zone around each explored state and uses scalable motion primitives whose sizes and curvatures adapt to local free space, guided by obstacle clearance $d^o$ and goal distance $d^g$. The key contributions are the effective zone formulation $r_i^e=\min(\kappa^o d^o_i, \kappa^g d^g_i)$, a mechanism for scaling motion primitives with $\eta_i$, and demonstrated efficiency gains over Weighted A* in clustered environments and near-goal refinement, with flexibility to incorporate heuristics. The approach yields substantially lower computation time and memory usage while preserving path optimality (or close to it), enabling real-time planning and robust performance in partially known or unknown environments.

Abstract

Path planning for a nonholonomic mobile robot is a challenging problem. This paper proposes a novel space adaptive search (SAS) approach that greatly reduces the computation cost of nonholonomic mobile robot path planning. The classic search-based path planning only updates the state on the current location in each step, which is very inefficient, and, therefore, can easily be trapped by local minimum. The SAS updates not only the state of the current location, but also all states in the neighborhood, and the size of the neighborhood is adaptively varied based on the clearance around the current location at each step. Since a great deal of states can be immediately updated, the search can explore the local minimum and get rid of it very fast. As a result, the proposed approach can effectively deal with clustered environments with a large number of local minima. The SAS also utilizes a set of predefined motion primitives, and dynamically scales them into different sizes during the search to create various new primitives with differing sizes and curvatures. This greatly promotes the flexibility of the search of path planning in more complex environments. Unlike the A* family, which uses heuristic to accelerate the search, the experiments shows that the SAS requires much less computation time and memory cost even without heuristic than the weighted A* algorithm, while still preserving the optimality of the produced path. However, the SAS can also be applied together with heuristic or other path planning algorithms.

Figures (18)

• Figure 1: The process of the A* algorithm trapped by the local minimum. The red branches show the trapped steps. Only after the local minimum has been fully explored, the search can finally go towards the goal. This drawback can seriously increase the computation time and cannot be avoided by simply inflating the heuristic, such as weighted A* algorithms.
• Figure 2: (a) 3D discrete state-space $S^3 =\{x, y, \theta\}$; (b) orientation space, $\theta_{min}$ is the minimum orientation step; (c) the motion primitives defined to sequentially land in different orientations.
• Figure 3: (a) The classic search based path planning algorithm only update the states at the current location; (b) updating all states in the effective zone can dramatically reduce the computation time, where the effective zone is the area centered on the current state.
• Figure 4: (a) The radius $r_i^e$ of the effective zone $\varOmega_i$ of $\zeta_i$ depends on the distance to its closest obstacle $d^o_i$ and its distance to the goal $d^g_i$; (b) the effective zone shrinks while the search is approaching the obstacle or the goal.
• Figure 5: (a) Grid map: the black cells represent the locations of obstacles; (b) the clearance map is transformed from the grid map with the distance transformation. Each cell is attached with a value representing the distance to its closest obstacle. This can be used as a measurement of the free space around the current location.