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: A game including a game board is provided with two recesses and including two sets of pieces which may be assembled to reconstitute two similar pictures, one picture within and filling each recess, the pieces of the two sets being of the same shape and size but each piece belonging to one set only and not the other by virtue of the pieces bearing non-interchangeable elements of pictures to be reconstituted. The puzzle may be played competitively, with two players racing against one another to complete pictures.