  In this paper, we tackle the problem of trajectory planning and control of a
vehicle under locally varying traction limitations, in the presence of suddenly
appearing obstacles. We employ concepts from adaptive model predictive control
for run-time adaptation of tire force constraints that are imposed by local
traction conditions. To solve the resulting optimization problem for real-time
control synthesis with such time varying constraints, we propose a novel
numerical scheme based on Real Time Iteration Sequential Quadratic Programming
(RTI-SQP), which we call Sampling Augmented Adaptive RTI (SAA-RTI). Sampling
augmentation of conventional RTI-SQP provides additional feasible candidate
trajectories for warmstarting the optimization procedure. Thus, the proposed
SAA-RTI algorithm enables real time constraint adaptation and reduces
sensitivity to local minima. Through extensive numerical simulations we
demonstrate that our method increases the vehicle's capacity to avoid accidents
in scenarios with unanticipated obstacles and locally varying traction,
compared to equivalent non-adaptive control schemes and traditional planning
and tracking approaches.
