In a MultibodyPlant, is there any way to specify that a body must follow a kinematic trajectory as a constraint (known positions/velocities at each time step, specified as a piecewise trajectory)? This is to ensure that a body in the MBP is constrainted to follow a given path with a specified timing, while other bodies follow the normal dynamics.
A similar question was answered: Does Drake have an equivalent of mujoco "mocap" bodies? by using high gains on a PD servo for each degree of freedom of the body. However, this seems to have unintended effects where the body lags behind the target trajectory, requires very small timesteps, or becomes numerical unstable.
The only other similar thing seems to be a CurvilinearJoint but this is limited to a plane and still needs forces since its a joint (with the similar high gain PD servo).
As of v1.43, no -- there is no implementation of prescribed motion. Feature request drake#19234 is the tracking issue.