Systems, methods, and computer-readable media for spatio-temporal motion planning

A system for motion planning for an autonomous vehicle, the system comprising one or more processors and a memory storing executable instructions that, when executed by the one or more processors configure the system to perform a method comprising:

• receiving data defining a drivable area within a spatio-temporal space that includes first and second spatial dimensions and a time dimension, the first and second spatial dimensions defining a spatial frame, the first spatial dimension and time dimension defining a first spatio-temporal frame, and the second spatial dimension and time dimension defining a second spatio-temporal frame;
• generating a set of constraints for a trajectory within the drivable area;
• generating a cost function to be minimized that includes one or more upper-bound cost terms, each upper-bound cost term approximating the upper-bound of a cost term for the trajectory for the spatial frame, each upper-bound cost term being expressed as one or more longitudinal-temporal cost terms for the trajectory for the first spatio-temporal frame and one or more lateral-temporal cost terms for the second spatio-temporal frame;
• computing, based on the set of constraints and the cost function, a planned trajectory through the drivable area, the planned trajectory directory being optimized with respect to each of the spatial frame, the first spatio-temporal frame and the second spatio-temporal frame;
• and
• outputting the planned trajectory for controlling an operation of the autonomous vehicle.

A non-transitory computer-readable medium storing instructions which, when executed by execution by a processing system, cause the processing system to perform a method comprising:

• receiving data defining a drivable area within a spatio-temporal space that includes first and second spatial dimensions and a time dimension, the first and second spatial dimensions defining a spatial frame, the first spatial dimension and time dimension defining a first spatio-temporal frame, and the second spatial dimension and time dimension defining a second spatio-temporal frame;
• generating a set of constraints for a trajectory within the drivable area;
• generating a cost function to be minimized that includes one or more upper-bound cost terms, each upper-bound cost term approximating the upper-bound of a cost term for the trajectory for the spatial frame, each upper-bound cost term being expressed as one or more longitudinal-temporal cost terms for the trajectory for the first spatio-temporal frame and one or more lateral-temporal cost terms for the second spatio-temporal frame;
• computing, based on the set of constraints and the cost function, a planned trajectory through the drivable area, the planned trajectory directory being optimized with respect to each of the spatial frame, the first spatio-temporal frame and the second spatio-temporal frame;
• and
• outputting the planned trajectory for controlling an operation of the autonomous vehicle.