We propose a learning-based trajectory tracking controller for autonomous robotic platforms whose motion can be described kinematically on $\mathrm{SE}(3)$. The controller is formulated in the dual quaternion framework and operates at the velocity level, assuming direct command of angular and linear velocities, as is standard in many aerial vehicles and omnidirectional mobile robots. Gaussian Process (GP) regression is integrated into a geometric feedback law to learn and compensate online for unknown, state-dependent disturbances and modeling imperfections affecting both attitude and position, while preserving the algebraic structure and coupling properties inherent to rigid-body motion. The proposed approach does not rely on explicit parametric models of the unknown effects, making it well-suited for robotic systems subject to sensor-induced disturbances, unmodeled actuation couplings, and environmental uncertainties. A Lyapunov-based analysis establishes probabilistic ultimate boundedness of the pose tracking error under bounded GP uncertainty, providing formal stability guarantees for the learning-based controller. Simulation results demonstrate accurate and smooth trajectory tracking in the presence of realistic, localized disturbances, including correlated rotational and translational effects arising from magnetometer perturbations. These results illustrate the potential of combining geometric modeling and probabilistic learning to achieve robust, data-efficient pose control for autonomous robotic systems.

翻译：本文提出一种基于学习的轨迹跟踪控制器，适用于运动学上可用$\mathrm{SE}(3)$描述的自主动力平台。该控制器在对偶四元数框架下构建，在速度层面运行，并假设可直接指令角速度与线速度——此假设符合多数飞行器与全向移动机器人的标准控制模式。我们将高斯过程回归融入几何反馈律中，在线学习并补偿影响姿态与位置的未知状态相关扰动及建模缺陷，同时保持刚体运动固有的代数结构与耦合特性。所提方法不依赖于未知效应的显式参数化模型，因此适用于受传感器诱导扰动、未建模执行耦合及环境不确定性影响的机器人系统。基于李雅普诺夫的分析证明了在有界高斯过程不确定性下位姿跟踪误差的概率极限有界性，为该学习型控制器提供了形式化的稳定性保证。仿真结果表明，在存在现实局部扰动（包括由磁力计扰动引起的相关旋转与平移效应）的情况下，控制器能实现精确平滑的轨迹跟踪。这些结果展示了结合几何建模与概率学习以实现自主机器人系统鲁棒、数据高效位姿控制的潜力。