Path planning shows great potential for exploring indoor and outdoor environments. In this paper, a probabilistic method is proposed to design path planners based on transition probabilistic matrices and signed distance functions. The transition probabilistic matrix is constructed by collecting path sequence data generated by performing a modified RRT with many times. Moreover, the signed distance function is introduced to simulate the safety coefficient which can guarantee a suitable distance between robots and obstacles. By combining the transition probability and the safety coefficient, our path planning task is modeled as a maximal probability sequence decision problem which in essence is equivalent to a minimal cost path problem, and then the dynamic programming solver is achieved by using the push-based efficient implementation of Bellman–Ford’s algorithm Kleinberg and Tardos (2006). Several path evaluation criteria are also used to evaluate path planning results, and plenty of experimental results illustrate the effectiveness of the proposed method.

路径规划显示出探索室内和室外环境的巨大潜力。本文提出了一种基于转移概率矩阵和有符号距离函数的概率方法来设计路径规划器。通过收集执行改进的RRT生成的路径序列数据来构造转移概率矩阵很多次。此外，引入有符号距离函数来模拟安全系数，该安全系数可以保证机器人与障碍物之间的适当距离。通过结合转移概率和安全系数，将我们的路径规划任务建模为一个最大概率序列决策问题，该问题本质上等效于最小成本路径问题，然后使用基于推式的有效算法来实现动态规划求解器。 Bellman-Ford算法的实现Kleinberg和Tardos（2006）。几种路径评估标准还用于评估路径规划结果，大量实验结果证明了该方法的有效性。