A Differentiable Dynamic Modeling Approach to Integrated Motion Planning and Actuator Physical Design for Mobile Manipulators

TL;DR

The paper develops a differentiable dynamic modeling framework for mobile manipulators with motor-parameterized actuators, enabling gradient-based co-design and integrated motion planning. By analytically linking motor geometry to torque and speed capabilities and embedding these into forward/inverse dynamics, the authors formulate an integrated locomotion-manipulation optimization solved via direct collocation. Key contributions include (i) an analytical motor torque/speed model parameterized by physically meaningful design variables, (ii) a differentiable, coupled base-arm dynamics model, (iii) an integrated planning formulation that outperforms sequential approaches in time efficiency and energy use, and (iv) a simultaneous actuator-design and motion-planning framework with numerical validation. The results show that differentiable motor-aware dynamics accelerate optimization, improve task completion time, and reduce energy consumption, highlighting the potential for offline co-design of mobile manipulators. The work lays a foundation for actuator-aware planning and design and points to future work on full 6-DOF bases, gearbox dynamics, and friction modeling to further enhance realism and applicability.

Abstract

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.

Figures (18)

• Figure 1: Definition of a mobile manipulator. Joint 3 to Joint $n+2$ are all 1-DOF joints; Joint e is only for notation and has 0-DOF.
• Figure 2: Scheme of a geared motor between Link $k-1$ and Link $k$ ($k=3, \cdots, n+2$).
• Figure 3: The cross-section of an SPMSM design. The core axial length $l$ is not illustrated in this figure.
• Figure 4: $i_{\mathrm{d,lim},j}$ as a function of $\omega_j$ in all cases. The blue lines represent the function $i_{\mathrm{d,lim},j}(\omega_j)$; the red dashed lines represent $I_{\mathrm{max},j}$; the pink dash-dot lines represent $\omega_{\mathrm{max},j}$ from \ref{['eq:omega_max']}. The intersection in (a) indicates the maximum motor speed constrained by the maximum current $I_{\mathrm{max},j}$.
• Figure 5: Visualization of current and voltage constraints in all cases given the same motor speed. Blue circles represent current constraints; contours represent voltage constraints; red cross marks represent centers of the voltage constraint contours; green (dashed) lines represent the max torque loci while increasing the motor speed.

Theorems & Definitions (5)

• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Remark 5