Humanoid robots with quasi-direct-drive actuators continuously generate joint torque while standing, whereas seated humans delegate weight support to chairs during desk work. As a first step toward seated loco-manipulation, we study omnidirectional seated locomotion on a passive mobile chair, requiring unfixed pelvis-seat contact and intermittent foot-floor propulsion of the robot-chair system. We extend a standard standing velocity-tracking environment with a passive-chair model, seated-state rewards, critic-only chair observations, and task-tailored contact settings. The policy is learned without motion-imitation rewards; its actor uses only proprioception and velocity commands, without contact sensing or chair states. In random-command evaluation, the policies tracked omnidirectional commands through nearly all 20-s rollouts, and the best seated policies could outperform the Standing policy in velocity tracking. Across four training seeds, a $2^3$ full-factorial comparison of symmetry regularization (SY), foot-slip regularization (FS), and command curriculum (CC) showed that FS reduced CoT but increased tracking error and that some FS-only policies converged to stationary local optima. Combining FS with either SY or CC avoided this failure without retuning FS, while SY improved bilateral leg symmetry during longitudinal motion. Direction-resolved analysis showed CoT ordered backward $<$ lateral $\ll$ forward, with planted-leg extension in backward and lateral motion and knee flexion following heel contact in forward motion. The learned policy achieved zero-shot sim-to-real transfer to a Unitree G1 and generated omnidirectional seated locomotion.

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