发表机构
University of Genoa; Shiraz University（热那亚大学; 设拉子大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出依赖参数的LMI框架，结合滑移干扰界等分析，使非完整移动机器人在可变地形的轨迹跟踪误差显著降低，具备良好稳定性与计算可行性。
AI 中文摘要
本文针对在可变地形表面上遭受严重乘性车轮滑移的非完整移动机器人的轨迹跟踪问题，提出了一种依赖参数的线性矩阵不等式（LMI）框架。该采样凸公式结合了网格到连续体的残差验证，同时确立了半全局微分输入到状态稳定性、规定的指数衰减率、区域极点配置以及针对执行器受限操作的增益有界反馈代理。核心贡献在于明确给出了Kanayama误差坐标中由有界乘性滑移诱导的加性干扰的上界，该上界搭建了物理滑移机制与凸综合范式之间的桥梁。辅助增益矩阵与逆存储度量以参考速度为仿射参数化，而存储度量则通过逐点矩阵求逆继承非线性依赖关系。稳定性通过结合变分收缩、前向不变性、滑移诱导干扰界以及基于耗散的轨迹重构的级联分析得以确立。数值验证在6条参考轨迹、6类干扰以及包含6处严重滑移斑块（双向滑移比达±50%）的60秒可变地形测试中对三种控制器进行了比较，该测试在两种几何构型上重复开展。补充研究涵盖高斯传感器噪声、复合压力测试以及嵌入式平台计算可行性。在100次蒙特卡洛运行中，所提出的控制器实现了在认证包络内的完整轨迹包含；在可变地形场景下，其峰值跟踪误差较固定增益LMI基准降低12%，较手动基准降低49%，而恒定增益基准在规定衰减率下不可行。
英文摘要
This paper presents a parameter-dependent linear matrix inequality (LMI) framework for trajectory tracking of nonholonomic mobile robots subject to severe multiplicative wheel slip on variable-terrain surfaces. The sampled convex formulation, augmented with grid-to-continuum residual certification, simultaneously establishes semi-global differential input-to-state stability, a prescribed exponential decay rate, regional pole placement, and a gain-bounded feedback proxy for actuator-limited operation. A central contribution is an explicit upper bound on the additive disturbance induced by bounded multiplicative slip in the Kanayama error coordinates, bridging the physical slip mechanism and the convex synthesis paradigm. The auxiliary gain matrix and inverse storage metric are parameterized affinely in the reference velocities, while the storage metric inherits nonlinear dependence through pointwise matrix inversion. Stability is established via a cascade analysis combining variational contraction, forward invariance, slip-induced disturbance bounds, and dissipation-based trajectory reconstruction. Numerical validation compares three controllers across six reference trajectories, six disturbance classes, and a 60-second variable-terrain test featuring six severe slip patches with bidirectional slip ratios reaching +/-50%, replicated on two geometries. Supplementary studies address Gaussian sensor noise, compound stress-testing, and embedded-platform computational feasibility. Across 100 Monte-Carlo runs the proposed controller achieves complete trajectory containment within the certified envelope. On the variable-terrain scenario, peak tracking error is reduced by 12% against the fixed-gain LMI baseline and 49% against the manual baseline, with the constant-gain baseline infeasible at the prescribed decay rate.
Comments23 pages, 18 figures, 50 references
