融合信念熵风险量化与改进A*算法的部分可观测环境路径规划

Path planning in partially observable environments by integrating belief entropy risk quantification and an improved A* algorithm

  • 摘要: 移动机器人在未知动态环境中行进时,感知不确定性与障碍物随机性常制约着规划的鲁棒性与实时性. 本文提出一种融合信念熵风险量化与改进A*算法的部分可观测环境路径规划框架. 首先,将导航任务建模为部分可观测马尔可夫决策过程(POMDP),通过贝叶斯概率推理维护环境信念状态;其次,重构A*评估函数,引入信念熵作为风险补偿项,实现路径代价与安全增益的协同优化,并结合三阶贝塞尔曲线提升轨迹平滑度. 针对大规模地图计算瓶颈,利用KD-tree结构优化邻域搜索,将碰撞检测复杂度由O(n)降至O(log n). 仿真实验表明:在50×50栅格场景下,所提算法平均单步决策时间仅为0.01 s,较POMCP算法提升逾两个数量级;在地图面积扩大9倍的压力测试中,峰值内存占用稳定在0.12 MB,展现了极佳的扩展性. 鲁棒性分析显示,在基础故障率 P_\texterr=0.5 的高噪声环境下,算法仍能保持65%的任务成功率,性能衰减斜率仅为–0.54. 可视化结果进一步验证了该框架在平衡避障安全性与目标收敛性方面的技术优势,为不确定环境下无人系统的实时稳健导航提供了有效方案.

     

    Abstract: Robot path planning in unknown and dynamic environments is frequently challenged by perceptual uncertainty and stochastic obstacles, which significantly constrain both navigation robustness and real-time responsiveness. To address these issues, this paper proposes a path planning framework for partially observable environments that integrates belief entropy–based risk quantification with an improved A* algorithm. First, the robot navigation problem is formulated as a partially observable Markov decision process (POMDP) that enables the robot to represent environmental uncertainty through probabilistic belief states. By employing Bayesian probabilistic inference, the system continuously updates its belief about the surrounding environment based on partial observations to maintain a probabilistic representation of obstacle distribution and reduce the impact of incomplete sensing information. This probabilistic representation allows the robot to reason about potential environmental risks and make more informed navigation decisions even when the available sensory information is incomplete or partially unreliable. On this basis, the traditional A* evaluation function is reconstructed by introducing belief entropy as a dynamic risk compensation term. This modification allows the algorithm to incorporate environmental uncertainty directly into the heuristic search process and enables the robot to jointly optimize path cost and safety gain during navigation. Compared with conventional heuristic search strategies that only consider the geometric distance or traversal cost, the proposed method introduces an uncertainty-aware planning mechanism that discourages the robot from passing through regions with high environmental ambiguity. In addition, third-order Bézier curves are used to smooth the generated paths, thereby improving trajectory continuity and making the planned routes more suitable for physical robotic platforms that require smooth motion control and kinematic feasibility. A k-dimensional tree spatial indexing structure is adopted to accelerate neighborhood searches during collision detection and obstacle querying to effectively reduce the computational complexity from O(n) to O(log n). Extensive simulation experiments are conducted to evaluate the performance of the proposed framework. Results show that in grid-based environments, the proposed algorithm achieves an average single-step decision time of approximately 0.01 s, which is more than two orders of magnitude faster than the classical POMCP algorithm. In scalability stress tests where the map area is expanded by nine times, the peak memory consumption remains stable at approximately 0.12 MB, demonstrating excellent scalability and suitability for resource-constrained embedded systems. Robustness analysis further indicates that even in high-noise environments with elevated sensor failure rates, the algorithm can still maintain a task success rate of approximately 65%, with a performance degradation slope of only −0.54, showing strong tolerance to perception uncertainty. Visualization results confirm that the proposed framework effectively balances obstacle avoidance safety and goal-directed convergence, allowing the robot to avoid uncertain regions while maintaining efficient progress toward the target. Overall, by integrating probabilistic belief modeling with efficient heuristic search, the proposed method provides a practical and computationally efficient solution for real-time robust navigation of unmanned robotic systems operating in uncertain and partially observable environments. It is particularly suitable for complex industrial and service robotics scenarios with significant uncertainty, dynamic disturbances, and limited onboard computational resources in current practical applications.

     

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