Track papers across labs, topics, and trends.
Search papers, labs, and topics across Lattice.
This paper addresses the challenge of stabilizing the kinematic bicycle model for car-like vehicles during parking maneuvers, which has been limited by existing feedback laws in Cartesian coordinates. By transforming the system into polar coordinates and incorporating range-normalized coordinates, the authors enable a backstepping design that overcomes Brockett's condition. The resulting smooth feedback laws achieve global exponential stabilization, producing realistic parking trajectories that mimic human drivers' behavior.
Transforming the kinematic bicycle model into polar coordinates unlocks smooth feedback laws that replicate human-like parking maneuvers.
At parking speeds, the kinematic bicycle is the prevailing model for car-like vehicles. Yet, despite its wide use, stabilizing feedback laws for this system are scarce in the literature, and existing designs often do not reproduce realistic parking maneuvers. This limitation is inherent to the Cartesian coordinates, where Brockett's condition rules out smooth static feedback stabilization. We bypass this obstruction by transforming the system into polar coordinates together with additional range-normalized coordinates that encode the geometry of human-like parking maneuvers. In the transformed coordinates, the dynamics take a strict-feedback form, enabling a nonconventional backstepping design. We exploit the particular structure to develop smooth feedback laws that achieve global exponential stabilization in the transformed coordinates which in turn generates parking trajectories resembling the one performed by human drivers through feedback alone.