# Trajectory Planning Under Vehicle Dimension Constraints Using Sequential Linear Programming

## TL;DR

This paper introduces a spatial-based trajectory planning method for automated vehicles that efficiently handles vehicle dimension constraints without inflating obstacles, using sequential linear programming to optimize paths in constrained environments.

## Contribution

It proposes a novel convex optimization approach that linearizes vehicle dimension constraints in a road-aligned frame, enabling effective trajectory planning without safety-margin inflation.

## Key findings

- Effective in very constrained environments
- Outperforms clothoid-based path planner in tight scenarios
- Maximizes performance by avoiding obstacle inflation

## Abstract

This paper presents a spatial-based trajectory planning method for automated vehicles under actuator, obstacle avoidance, and vehicle dimension constraints. Starting from a nonlinear kinematic bicycle model, vehicle dynamics are transformed to a road-aligned coordinate frame with path along the road centerline replacing time as the dependent variable. Space-varying vehicle dimension constraints are linearized around a reference path to pose convex optimization problems. Such constraints do not require to inflate obstacles by safety-margins and therefore maximize performance in very constrained environments. A sequential linear programming (SLP) algorithm is motivated. A linear program (LP) is solved at each SLP-iteration. The relation between LP formulation and maximum admissible traveling speeds within vehicle tire friction limits is discussed. The proposed method is evaluated in a roomy and in a tight maneuvering driving scenario, whereby a comparison to a semi-analytical clothoid-based path planner is given. Effectiveness is demonstrated particularly for very constrained environments, requiring to account for constraints and planning over the entire obstacle constellation space.