Abstract: Systems and techniques for determining a sideslip vector for a vehicle that may have a direction that is different from that of a heading vector for the vehicle. The sideslip vector in a current vehicle state and sideslip vectors in predicted vehicles states may be used to determine paths for a vehicle through an environment and trajectories for controlling the vehicle through the environment. The sideslip vector may be based on a vehicle position that is the center point of the wheelbase of the vehicle and may include lateral velocity, facilitating the control of four-wheel steered vehicle while maintaining the ability to control two-wheel steered vehicles.

Abstract: Techniques for determining vehicle trajectories to operate a vehicle according to a planned path are described herein. In an example, a vehicle computing system may determine a location of the vehicle at a first time. Based on the location, the vehicle computing system may determine an estimated location of the vehicle at a second time, the estimated location of the vehicle including a lateral coordinate and a longitudinal coordinate. The vehicle computing system may determine the longitudinal coordinate based on a vehicle trajectory associated with the first time (e.g., previously determined trajectory) and the lateral coordinate based on the planned path. The vehicle computing system may determine a second vehicle trajectory based in part on the estimated location and the first trajectory, and may control the vehicle according to the second vehicle trajectory.