Xincheng Cao, Haochong Chen, Bilin Aksun-Guvenc, Levent Guvenc Automated Driving Lab, Ohio State University Brian Link, Peter J Richmond, Dokyung Yim, S hihong Fan, John Harber HATCI Abstract Reverse parking maneuvers of a vehicle with trailer system is a challenging task to complete for human drivers due to the unstable nature of the system and unintuitive controls required to orientate the trailer properly. This paper hence proposes an optimization-based automation routine to handle the path-planning and path-tracking control process of such type of maneuvers. The proposed approach utilizes nonlinear model predictive control (NMPC) to robustly guide the vehicle-trailer system into the desired parking space, and an optional forward repositioning maneuver can be added as an additional stage of the parking process to obtain better system configurations, before backward motion can be attempted again to get a good final pose . The novelty of the proposed approach is the simplicity of its formulation, as the path -planning and path-tracking operations are only conducted on the trailer being viewed as a standalone vehicle, before the control inputs are propagated to the tractor vehicle via inverse kinematic relationships also derived in this paper. Simulation case studies and hardware-in -the -loop tests are performed, and the results demonstrate the efficacy of the proposed approach. In troduction The development of connected and autonomous or automated vehicles has seen much progress in recent years [1-9] . One of the most important functions of such vehicles is to plan and track their own paths [10], [ 11].

Trailer parking is a challenging task due to the unstable nature of the vehicle-trailer system in reverse motion and the unintuitive steering actions required at the vehicle to accomplish the parking maneuver. This paper presents a strategy to tackle this kind of maneuver with an advisory graphic aid to help the human driver with the task of manually backing up the vehicle-trailer system. A kinematic vehicle-trailer model is derived to describe the low-speed motion of the vehicle-trailer system, and its inverse kinematics is established by generating an equivalent virtual trailer axle steering command. The advisory system graphics is generated based on the inverse kinematics and displays the expected trailer orientation given the current vehicle steer angle and configuration (hitch angle). Simulation study and animation are set up to test the efficacy of the approach, where the user can select both vehicle speed and vehicle steering angle freely, which allows the user to stop the vehicle-trailer system and experiment with different steering inputs to see their effect on the predicted trailer motion before proceeding with the best one according to the advisory graphics, hence creating a series of piecewise continuous control actions similar to how manual trailer reverse parking is usually carried out. The advisory graphics proves to provide the driver with an intuitive understanding of the trailer motion at any given configuration (hitch angle).

Jackknifing refers to the serious situation where a vehicle-trailer system enters a jackknife state and the vehicle and trailer eventually collide if trailer operation is not corrected. This paper considers low speed trailer maneuvering typical of trailer backing where jackknife state limits can vary due to sideslip caused by physical interaction between the vehicle, trailer, and environment. Analysis of a kinematic model considering sideslip at the vehicle and trailer wheels indicates that vehicle-trailer systems should be divided into three categories based on the ratio of hitch length and trailer tongue length, each with distinct behaviors. The Long Trailer category may have no jackknifing state while the other two categories always have states leading to jackknifing. It is found that jackknife limits, which are the boundaries between the jackknifing state and the recoverable regions, can be divided into safe and unsafe limits, the latter of which must be avoided. Simulations and physical experiments support these results and provide insight about the implications of vehicle and trailer states with slip that lead to jackknifing. Simulations also demonstrate the benefit of considering these new slip-based jackknife limits in trailer backing control.