This paper investigates the differentiable dynamic modeling of mobile manipulators to facilitate efficient motion planning and physical design of actuators, where the actuator design is parameterized by physically meaningful motor geometry parameters. These parameters impact the manipulator's link mass, inertia, center-of-mass, torque constraints, and angular velocity constraints, influencing control authority in motion planning and trajectory tracking control. A motor's maximum torque/speed and how the design parameters affect the dynamics are modeled analytically, facilitating differentiable and analytical dynamic modeling. Additionally, an integrated locomotion and manipulation planning problem is formulated with direct collocation discretization, using the proposed differentiable dynamics and motor parameterization. Such dynamics are required to capture the dynamic coupling between the base and the manipulator. Numerical experiments demonstrate the effectiveness of differentiable dynamics in speeding up optimization and advantages in task completion time and energy consumption over established sequential motion planning approach. Finally, this paper introduces a simultaneous actuator design and motion planning framework, providing numerical results to validate the proposed differentiable modeling approach for co-design problems.

翻译：本文研究了移动机械臂的可微动力学建模，以促进高效的执行器运动规划与物理设计。其中执行器设计由具有物理意义的电机几何参数表征，这些参数影响机械臂的连杆质量、惯性、质心、转矩约束和角速度约束，从而影响运动规划与轨迹跟踪控制中的控制权限。通过解析建模电机最大转矩/速度及其设计参数对动力学特性的影响，实现了可微解析动力学建模。进一步，基于所提出的可微动力学与电机参数化方法，采用直接配点离散化构建了统一的移动与操作规划问题。此类动力学模型需要捕捉移动基座与机械臂之间的动态耦合效应。数值实验验证了可微动力学在加速优化求解方面的有效性，以及在任务完成时间与能耗上相较于传统顺序运动规划方法的优势。最后，本文提出了执行器设计与运动规划的协同优化框架，通过数值结果验证了所提可微建模方法在联合设计问题中的有效性。