  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.
