Path optimization is not included and will be added further.

Similar path planning algorithms for a car pulling trailer are discussed by Habrador and Atsushi Sakai

The difference is that hitch point can be set not only at the midpoint of rear axle but also at the rear point of car body, more general for a car pulling a trailer.

Ref:

• Practical Search Techniques in Path Planning for Autonomous Driving

• Application of Hybrid A* to an Autonomous Mobile Robot for Path Planning in Unstructured Outdoor Environments

Here the modus operandi of exact input/output linearization technique is used to calculate the steering wheel angle.

Ref:

• Reversing the General One-Trailer System: Asymptotic Curvature Stabilization and Path Tracking

Two different state space equations are applied for path tracking.

Compared to steering angle, the steering angle rate as controlled signal can make system more stable. It can be found in following figures.

Ref:

• Obstacle Avoidance Using Adaptive Model Predictive Control

Here nonlinear model predictive control is used to calculate the steering wheel angle.

Ref:

• Nonlinear model predictive controller

MIT

• Junyu Zhou