  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.
