  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.
