# Adaptive Trajectory Planning and Optimization at Limits of Handling

## TL;DR

This paper introduces a real-time adaptive trajectory planning method for vehicles that accounts for local traction variations and obstacles, improving safety and obstacle avoidance capabilities.

## Contribution

It proposes a novel SAA-RTI algorithm that enhances real-time control by adaptively handling traction constraints and avoiding local minima.

## Key findings

- Increased vehicle safety in obstacle-rich, traction-variable scenarios.
- Enhanced real-time trajectory feasibility and robustness.
- Superior performance over non-adaptive control schemes.

## Abstract

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.