Abstract: Aspects of the disclosure relate to controlling a vehicle having an autonomous driving mode or an autonomous vehicle. For instance, a polygon representative of the shape and location of a first object may be received. A polyline contour representation of a portion of a polygon representative of the shape and location of a second object may be received. The polyline contour representation may be in half-plane coordinates and including a plurality of vertices and line segments. Coordinates of the polygon representative of the first object may be converted to the half-plane coordinate system. A collision location between the polyline contour representation and the polygon representative of the first object may be determined using the converted coordinates. The autonomous vehicle may be controlled in the autonomous driving mode to avoid a collision based on the collision location.

Abstract: Aspects and implementations of the present disclosure relate to modeling of positional uncertainty of moving objects using precomputed polygons, for example, for the purposes of computing autonomous vehicle (AV) trajectories. An example method includes: receiving, by a data processing system of an AV, data descriptive of an agent state of an object; generating a polygon representative of the agent state; identifying extreme vertices of the polygon along a longitudinal axis parallel to a heading direction of the object or along a lateral axis orthogonal to the heading direction; and applying, based on the extreme vertices, at least one expansion transformation to the polygon along the longitudinal axis or the lateral axis to generate a precomputed polygon.

Abstract: Aspects of the disclosure provide for controlling an autonomous vehicle. For instance, data identifying an object may be received. A first portion of a trajectory may be generated using a first uncertainty distribution for the object. The first portion of the trajectory may enable the autonomous vehicle to make progress towards a destination of the autonomous vehicle. A fallback portion of the trajectory may be generated using a second uncertainty distribution for the object. The fallback portion may enable the autonomous vehicle to stop. The second uncertainty distribution may be different from the first uncertainty distribution, and the second uncertainty distribution may be based on a predetermined uncertainty distribution if the autonomous vehicle loses a localization improvement process. The autonomous vehicle may be controlled according to the trajectory.

Abstract: Aspects of the disclosure provide for controlling an autonomous vehicle. For instance, a trajectory for the autonomous vehicle to traverse in order to follow a route to a destination may be generated. A first error value for a boundary of an object, a second error value for a location of the autonomous vehicle, a third error value for a predicted future location of the object may be received. An uncertainty value for the object may be determined by combining the first error value, the second error value, and the third error value. A lateral gap threshold for the object may be determined based on the uncertainty value. The autonomous vehicle may be controlled in an autonomous driving mode based on the lateral gap threshold for the object.

Abstract: Aspects and implementations of the present disclosure relate to modeling of positional uncertainty of moving objects using precomputed polygons, for example, for the purposes of computing autonomous vehicle (AV) trajectories. An example method includes: receiving, by a data processing system of an AV, data descriptive of an agent state of an object; generating a polygon representative of the agent state; identifying extreme vertices of the polygon along a longitudinal axis parallel to a heading direction of the object or along a lateral axis orthogonal to the heading direction; and applying, based on the extreme vertices, at least one expansion transformation to the polygon along the longitudinal axis or the lateral axis to generate a precomputed polygon.

Abstract: Aspects and implementations of the present disclosure relate to autonomous vehicle (AV) trajectories computed using a box-based probabilistic overlap model. An example method includes: receiving, by a data processing system of an AV, data descriptive of an agent state of an object relative to the AV; computing an initial overlap region between a first box representative of the AV and a second box representative of the agent state; updating dimensions of the second box; and computing an updated overlap region by interpolating the initial overlap region based on the updated dimensions of the second box.

Abstract: Aspects of the disclosure relate to controlling a vehicle having an autonomous driving mode or an autonomous vehicle. For instance, a polygon representative of the shape and location of a first object may be received. A polyline contour representation of a portion of a polygon representative of the shape and location of a second object may be received. The polyline contour representation may be in half-plane coordinates and including a plurality of vertices and line segments. Coordinates of the polygon representative of the first object may be converted to the half-plane coordinate system. A collision location between the polyline contour representation and the polygon representative of the first object may be determined using the converted coordinates. The autonomous vehicle may be controlled in the autonomous driving mode to avoid a collision based on the collision location.

Abstract: Aspects of the disclosure relate to controlling a vehicle having an autonomous driving mode or an autonomous vehicle. For instance, a polygon representative of the shape and location of a first object may be received. A polyline contour representation of a portion of a polygon representative of the shape and location of a second object may be received. The polyline contour representation may be in half-plane coordinates and including a plurality of vertices and line segments. Coordinates of the polygon representative of the first object may be converted to the half-plane coordinate system. A collision location between the polyline contour representation and the polygon representative of the first object may be determined using the converted coordinates. The autonomous vehicle may be controlled in the autonomous driving mode to avoid a collision based on the collision location.

Abstract: Aspects of the disclosure relate to controlling a vehicle having an autonomous driving mode or an autonomous vehicle. For instance, a polygon representative of the shape and location of a first object may be received. A polyline contour representation of a portion of a polygon representative of the shape and location of a second object may be received. The polyline contour representation may be in half-plane coordinates and including a plurality of vertices and line segments. Coordinates of the polygon representative of the first object may be converted to the half-plane coordinate system. A collision location between the polyline contour representation and the polygon representative of the first object may be determined using the converted coordinates. The autonomous vehicle may be controlled in the autonomous driving mode to avoid a collision based on the collision location.

Abstract: Apparatus and method for the treatment of pollutants in gases which includes a plasma reactor chamber having sawtooth electrodes through which said gases flow, a generator of high voltage pulses of short width, high repetition rate and rapid rise time being coupled to said reactor with matched impedance, causing pulsed streamer discharges to be initiated at said chamber electrodes, increasing the effective plasma volume for more efficient pollutant reduction.