Abstract: This paper studies the real-time motion planning problem for steerable-wheeled mobile robots (SWMRs). Despite significant progress in SWMR control, most existing approaches design controllers for specific task scenarios and actuator limitations, and are further restricted to four-wheel rectangular layouts, resulting in limited versatility. Motivated by these issues, we formulate SWMR motion planning as an optimization problem that simultaneously maximizes motion performance while enforcing actuator feasibility. The proposed formulation supports flexible combinations of task objectives, wheel placements, and actuator constraints without modifying the underlying framework.
Formulation alone does not guarantee real-time solvability; we therefore design a tailored fast algorithm that iteratively contracts the non-convex feasible set toward stationary points. Although contraction-based iterations are uncommon, their anytime feasibility and computational efficiency make them particularly suitable for real-time robotic applications. We then rigorously establish the descent, convergence, and feasibility properties of the proposed algorithm. Simulation results on a trajectory tracking task demonstrate an order-of-magnitude reduction in computation time and great improvement in constraint satisfaction compared to baseline methods.