基于动态走廊膨胀与凸优化的移动机器人分层运动规划

doi:10.16182/j.issn1004731x.joss.25-0395

摘要/Abstract

摘要：

阿克曼底盘机器人在动态复杂环境中的运动规划面临着非完整性约束与运动动力学耦合挑战，为解决传统方法存在着路径冗余、随机性波动及局部最优等共性问题，提出基于动态走廊膨胀与凸优化的分层运动规划方法。基于融合RDP（Ramer-Douglas-Peucke）路径压缩算子与A*算法生成拓扑稀疏路径，有效降低冗余路径点对后端优化的干扰。结合阿克曼转向特性设计动态走廊膨胀策略，通过凸分解技术构建符合阿克曼机器人运动学约束的安全走廊。将走廊约束转化为线性不等式嵌入凸优化模型，采用加速度二阶导数最小化目标函数，并引入曲率自适应时间调整机制实现动力学约束下的全局最优轨迹生成。仿真数据表明：在密集障碍物场景中成功率达97.3%，相较于A*算法轨迹平滑度提升93.5%、路径点数减少81.6%，相较于结合A*及共轭梯度优化算法平滑度提升91.6%、路径点数降低81.8%；通过高精度iGPS定位系统开展实物验证，厘米级轨迹跟踪结果证实了算法与控制系统的实际适配性。该方法显著提升了阿克曼机器人在仓储物流、城市救援等动态场景下的规划质量与执行可靠性，为解决非完整移动平台的运动规划问题提供了新的技术路径。

关键词: 阿克曼机器人, 运动规划, 安全走廊, 轨迹优化, 凸优化

Abstract:

Motion planning for robots with Ackermann chassis in dynamic complex environments faces nonholonomic constraints and kinematic-dynamic coupling challenges. However, traditional methods suffer from path redundancy, random fluctuations, and local optimality. A hierarchical motion planning method based on dynamic corridor inflation and convex optimization is proposed. Topologically sparse paths are generated by fusing the Ramer-Douglas-Peucker (RDP) path compression operator with the A* algorithm to reduce redundant path points' interference with backend optimization. Dynamic corridor inflation strategies are designed considering Ackermann steering characteristics, and safe corridors satisfying kinematic constraints are constructed via convex decomposition. Corridor constraints are then transformed into linear inequalities embedded in a convex optimization model. An objective function of minimizing acceleration's second derivative is adopted, and a curvature-adaptive time adjustment mechanism is introduced for global optimal trajectory generation under dynamic constraints. Simulation and physical verification platforms validate the algorithm's effectiveness. In scenarios with dense obstacles, it achieves a 97.3% success rate. Compared with the A* algorithm, it improves trajectory smoothness by 93.5% and reduces 81.6% of path points. In comparison with hierarchical motion planning method with A*-integrated ESDF-based conjugate gradient optimization (HPGO), the proposed method enhances trajectory smoothness by 91.6% and reduces 81.8% of path points. High-precision iGPS physical tests show centimeter-level tracking accuracy, confirming algorithm-control system adaptability. Experiments demonstrate improved planning quality and execution reliability in warehouse logistics, urban rescue, etc., offering a new solution for nonholonomic mobile platform motion planning.

Key words: Ackermann-steering robots, motion planning, safe corridors, trajectory optimization, convex optimization

中图分类号:

TP242

张定坤,梁海朝 . 基于动态走廊膨胀与凸优化的移动机器人分层运动规划[J]. 系统仿真学报, 2026, 38(5): 1383-1407.

Zhang Dingkun,Liang Haizhao . Hierarchical Motion Planning of Mobile Robot Based on Dynamic Corridor Inflation and Convex Optimization[J]. Journal of System Simulation, 2026, 38(5): 1383-1407.

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表1

算法效果量化对比

量化指标	HPCC	HPGO	A*
曲线连续性误差 $/ (r a d / m 2)$	70.32	837.65	1 082.84
轨迹长度/m	29.74	30.59	30.64
重规划计算时间/ms	93.11	80.79	65.77
路径点数量	100	543	544

表1

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表2

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参数名称	数据
尺寸/mm	445×359×206
重量/kg	9.34
续航时间/h	8.5
核心控制器	STM32F407VET6 ARM架构Cortex-M4内核32位