Slip-Induced Fall Suppression During Cornering for a Remotely Operated Motorcycle with a Rear-Wheel-Swing Mechanism

Foot slip is a major source of instability in bipedal locomotion on low-friction or uncertain terrain. Standard control approaches typically assume no-slip contact and therefore degrade when slip occurs. We propose a control framework that explicitly incorporates slip into the locomotion model through virtual nonholonomic constraints, which regulate the tangential stance-foot velocity while remaining compatible with the virtual holonomic constraints used to generate the walking gait. The resulting closed-loop system is formulated as a hybrid dynamical system with continuous swing dynamics and discrete impact events. A nonlinear feedback law enforces both classes of constraints and yields a slip-compatible hybrid zero dynamics manifold for the reduced-order locomotion dynamics. Stability of periodic walking gaits is characterized through the associated Poincaré map, and numerical results illustrate stabilization under slip conditions.

This paper presents a parameter-dependent linear matrix inequality (LMI) framework for trajectory tracking of nonholonomic mobile robots subject to severe multiplicative wheel slip on variable-terrain surfaces. The sampled convex formulation, augmented with grid-to-continuum residual certification, simultaneously establishes semi-global differential input-to-state stability, a prescribed exponential decay rate, regional pole placement, and a gain-bounded feedback proxy for actuator-limited operation. A central contribution is an explicit upper bound on the additive disturbance induced by bounded multiplicative slip in the Kanayama error coordinates, bridging the physical slip mechanism and the convex synthesis paradigm. The auxiliary gain matrix and inverse storage metric are parameterized affinely in the reference velocities, while the storage metric inherits nonlinear dependence through pointwise matrix inversion. Stability is established via a cascade analysis combining variational contraction, forward invariance, slip-induced disturbance bounds, and dissipation-based trajectory reconstruction. Numerical validation compares three controllers across six reference trajectories, six disturbance classes, and a 60-second variable-terrain test featuring six severe slip patches with bidirectional slip ratios reaching +/-50%, replicated on two geometries. Supplementary studies address Gaussian sensor noise, compound stress-testing, and embedded-platform computational feasibility. Across 100 Monte-Carlo runs the proposed controller achieves complete trajectory containment within the certified envelope. On the variable-terrain scenario, peak tracking error is reduced by 12% against the fixed-gain LMI baseline and 49% against the manual baseline, with the constant-gain baseline infeasible at the prescribed decay rate.

Real-world collision avoidance is a core motivation for studying the dynamics and control of high sideslip drifting in vehicles, yet the practical benefit of such maneuvers has so far primarily been tested in scenarios explicitly engineered to require drifting. In this work, we explore the question of if and when drifting may be optimal for safety in real-world winter driving conditions. We present a drift-capable nonlinear model predictive control (MPC) system designed to handle scenarios grounded in crash fatality data and deploy the controller in a high fidelity simulator across road departure and oncoming vehicle collision avoidance scenarios. The controller naturally initiates and sustains drifting maneuvers to stay on the road when hitting a patch of ice on the rear axle and to avoid an oncoming vehicle that has slid into its lane. Comparisons with a benchmark electronic stability control (ESC) system demonstrate how a drift-capable controller can trade off stability for controllability to precisely maneuver through dangerous winter driving scenarios. A Monte Carlo study over random ice patches further shows that the drift-capable controller achieves lower median lane error than ESC across several speeds, while revealing that drifting emerges predominantly at higher speeds.