Mismatch-Aware Adaptive Constraint Tightening for Bicycle-Model Trajectory Optimization

Trajectory optimization for autonomous vehicles usually relies on the kinematic bicycle model because of its computational simplicity. However, when the planned trajectory is executed under the true vehicle dynamics, which include lateral slip, tire stiffness and yaw-lateral coupling, safety constraints can be violated owing to the model mismatch. In this paper, we make three theoretical contributions. First, we derive a characteristic speed $v_c=\sqrt{C_αL/M}$ which separates two different mismatch regimes: below $v_c$ the dynamic bicycle initially oversteers inward (safe); above $v_c$ it understeers outward (safety-critical). Second, we prove that the peak outward deviation $\varepsilon^*$ follows a $T^2$ horizon scaling whose coefficient transitions between a transient bound $\frac{1}{2}(v^2-v_c^2)κ$ and a steady-state bound. Third, we obtain a simulation-free analytical coefficient $a_2^{\mathrm{anal}}=\frac{1}{2}(1-v_c^2/v_{\max}^2)T^2$ that is computable from vehicle parameters and the planning horizon alone. Putting these together, we propose Mismatch-Aware Adaptive Constraint Tightening (MACT), $ε(v,κ)=a_2 v^2|κ|$, which replaces a fixed worst-case margin by a state-dependent one that is large at high speed/curvature but nearly zero on gentle paths. Eight numerical experiments confirm the scaling laws. MACT reaches 100% safety with 84% less wasted margin than a fixed-margin baseline on the 2-DOF vehicle, extends to a nonlinear leaning bicycle, and in a closed-loop direct-shooting MPC comparison it cuts the applied margin by 34% compared with tube MPC while keeping the same safety.

On the Emergence of Pendular Structure in Multi-Contact Locomotion

LIPM is everywhere in legged-locomotion control, but almost always as a modeling choice rather than as something the controller's cost actually prefers. This note tries to make that link more explicit. Working from a small centroidal OCP that penalizes the rate of angular momentum, we look at what its optimum tends to look like. Three things come out. With full-rank stance, the optimum drifts toward a pendular force pattern at a rate determined by the SVD of the moment Jacobian; the constant is set by foot-span geometry and matches the experiments to within 16%. With N=2 stance, as in trot, the friction cone introduces a lower bound on $\|\dot{H}_G\|$ that no amount of weight tuning fixes; we also see a non-smooth feasibility kink at a critical horizontal acceleration that we can write in closed form. Adding a task term that asks for a nonzero $\dot{H}_G$ moves the optimum off the pendular set in a predictable way. None of this is far from the classical ZMP/DCM picture. We test these claims on a point-mass quadruped and on the Unitree Go1 in MuJoCo (open-loop QP and a torque-level closed-loop controller), and we note where the asymptotic story stops being a good description of what the closed loop actually does.

AeroBridge-TTA: Test-Time Adaptive Language-Conditioned Control for UAVs

Language-guided unmanned aerial vehicles (UAVs) often fail not from bad reasoning or perception, but from execution mismatch: the gap between a planned trajectory and the controller's ability to track it when the real dynamics differ from training (mass changes, drag shifts, actuator delay, wind). We propose AeroBridge-TTA, a language-conditioned control pipeline that targets this gap with test-time adaptation. It has three parts: a language encoder that maps the command into a subgoal, an adaptive policy conditioned on the subgoal and a learned latent, and a test-time adaptation (TTA) module that updates the latent online from observed transitions. On five language-conditioned UAV tasks under 13 mismatch conditions with the same domain randomization, AeroBridge-TTA ties a strong PPO-MLP baseline in-distribution and wins all 5 out-of-distribution (OOD) conditions, +22.0 pts on average (62.7% vs. 40.7%); the +8.5 pt overall gain comes entirely from the OOD regime. A same-weights ablation that only changes the step size $α$ shows the latent update itself is responsible for a $4.6\times$ OOD lift.