Collision-free motion generation
Apparatuses, systems, and techniques to perform collision-free motion generation (e.g., to operate a real-world or virtual robot). In at least one embodiment, at least a portion of the collision-free motion generation is performed in parallel.
1 . A method comprising:
using at least one first parallel processing unit (“PPU”) to generate a plurality of seed trajectories in parallel based at least in part on an initial joint configuration and a plurality of seed joint configurations that would position at least a portion of a first manipulator in a goal pose;
using at least one second PPU to modify the plurality of seed trajectories in parallel to obtain a plurality of modified trajectories;
selecting one of the plurality of modified trajectories based at least in part on cost values calculated for the plurality of modified trajectories; and
providing a motion plan based at least in part on the selected modified trajectory to a second manipulator to cause the second manipulator to move in accordance with the motion plan.
2 . The method of claim 1 , wherein using the at least one second PPU to modify the plurality of seed trajectories comprises, for a particular one of the plurality of seed trajectories, performing one or more iterations until at least one stopping condition is satisfied, each of the one or more iterations comprising performing at least one optimization on the particular seed trajectory.
3 . The method of claim 2 , wherein the at least one optimization comprises a gradient-free optimization, and a gradient-based optimization.
4 . The method of claim 3 , wherein the gradient-free optimization comprises a particle-based optimization.
5 . The method of claim 3 , wherein the gradient-based optimization is based at least in part on a Limited-memory Broyden-Fletcher-Goldfarb-Shanno (“L-BFGS”) algorithm.
6 . The method of claim 2 , wherein each of the one or more iterations comprises calculating a task cost, and
the at least one stopping condition is satisfied based at least in part on a comparison between the task cost and a threshold value.
7 . The method of claim 2 , wherein the at least one stopping condition is satisfied when at least a desired number of iterations have been performed.
8 . The method of claim 1 , wherein using the at least one first PPU to generate the plurality of seed trajectories in parallel comprises:
using inverse kinematics to obtain the plurality of seed joint configurations;
using at least one third PPU to modify the plurality of seed joint configurations to obtain a plurality of modified joint configurations; and
interpolating between the initial joint configurations and the plurality of modified joint configurations to obtain at least a portion of the plurality of seed trajectories.
9 . The method of claim 8 , wherein using the at least one third PPU to modify the plurality of seed joint configurations comprises, for a particular one of the plurality of seed joint configurations, performing one or more iterations until at least one stopping condition is satisfied, each of the one or more iterations comprising performing at least one optimization on the particular seed joint configuration.
10 . The method of claim 1 , wherein using the at least one first PPU to generate the plurality of seed trajectories in parallel comprises:
using geometric planning to obtain at least a portion of the plurality of seed trajectories.
11 . The method of claim 1 , wherein the second manipulator is the first manipulator.
12 . The method of claim 1 , wherein using the at least one second PPU to optimize the plurality of seed trajectories comprises, for a particular one of the plurality of seed trajectories, performing one or more iterations until at least one stopping condition is satisfied, each of the one or more iterations comprising:
performing at least one optimization on the particular seed trajectory to obtain optimization results comprising a number of steps having a previous step size,
obtaining a new step size determined based at least in part on at least one limitation of a device to perform the selected optimized trajectory, the selected optimized trajectory; and
scaling the selected optimized trajectory to comprise the number of steps having the new step size.
13 . The method of claim 12 , wherein the at least one limitation comprises at least one velocity constraint, at least one acceleration constraint, or at least one jerk constraint.
14 . The method of claim 12 , wherein each of the one or more iterations comprises:
calculating a task cost based at least in part on one or more constituent cost values; and
modifying at least a portion of the one or more constituent cost values based at least in part on a new time step.
15 . A system comprising:
one or more circuits to:
generate a plurality of seed trajectories in parallel based at least in part on an initial joint configuration and a plurality of seed joint configurations that would position at least a portion of a first manipulator in a goal pose,
calculate cost values for a plurality of modified trajectories obtained by modifying the plurality of seed trajectories in parallel, and
select a modified trajectory of the plurality of modified trajectories based at least in part on the cost values; and
a second manipulator to move in accordance with the selected modified trajectory.
16 . The system of claim 15 , wherein the second manipulator is different from the first manipulator.
17 . The system of claim 15 , wherein the second manipulator is at least a portion of an autonomous device or a semi-autonomous device.
18 . The system of claim 15 , wherein the second manipulator is at least a portion of an autonomous vehicle, an aerial drone, a cleaning device, a legged robot, or a walking robot.
19 . The system of claim 15 , wherein the one or more circuits are to modify a particular one of the plurality of seed trajectories by performing one or more iterations until at least one stopping condition is satisfied, each of the one or more iterations comprising performing a gradient-free optimization on the particular seed trajectory to obtain first optimization results, and performing a gradient-based optimization on the first optimization results to obtain second optimization results.
20 . The system of claim 15 , wherein the one or more circuits are to generate the plurality of seed trajectories in parallel by:
using inverse kinematics to obtain the plurality of seed joint configurations;
modifying the plurality of seed joint configurations to obtain a plurality of modified joint configurations; and
interpolating between the initial joint configurations and the plurality of modified joint configurations to obtain at least a portion of the plurality of seed trajectories.
21 . The system of claim 15 , wherein the one or more circuits are to generate at least a portion of the plurality of seed trajectories in parallel using geometric planning.
22 . The system of claim 21 , wherein the geometric planning comprises:
identifying at least one collision fee path segment by searching along directions between at least one vertex of a graph and a plurality of target points in the graph in parallel for at least one endpoint that does not collide with any obstacles;
adding to the graph at least one new vertex corresponding to the at least one endpoint; and
adding to the graph at least one new edge between the at least one vertex and the at least one new vertex.
23 . The system of claim 15 , wherein the one or more circuits are to generate a motion plan based at least in part on the selected modified trajectory and the second manipulator that is to move in accordance with the motion plan.
24 . The system of claim 15 , wherein the one or more circuits are to modify a particular one of the plurality of seed trajectories by performing one or more iterations until at least one stopping condition is satisfied, each of the one or more iterations comprising performing at least one optimization on the particular seed trajectory, the at least one optimization comprising calculating a collision cost value associated with one or more collisions encountered along the particular seed trajectory.
25 . The system of claim 24 , wherein calculating the collision cost value comprises:
determining a new position for a virtual object positioned at a third position between first and second positions, the new position being based at least in part on the third position and a first distance between the third position and a selected first virtual obstacle when the virtual object is not in a collision at the third position; and
until the virtual object would be positioned at a desired position with respect to at least one of the first position and the second position when the virtual object is positioned at the new position:
if the first distance is not greater than a second distance based at least in part on the new position and the desired position, calculating a collision cost if the virtual object would collide with at least one second virtual obstacle when the virtual object is at the new position, the new position being a previous position,
redetermining the first distance between the previous position and a selected second virtual obstacle, and
redetermining the new position based on the previous position and the first distance.
26 . The system of claim 15 , wherein the one or more circuits are to modify a particular one of the plurality of seed trajectories by performing one or more iterations until at least one stopping condition is satisfied, each of the one or more iterations comprising performing at least one optimization on the particular seed trajectory, the at least one optimization comprising calculating a collision cost value associated with one or more collisions encountered between components of a device moving in accordance with the particular seed trajectory.
27 . The system of claim 26 , wherein calculating the collision cost value comprises:
identifying as a set of movable objects any pairs of smaller objects representing the device that include first and second objects that are movable with respect to one another;
calculating distances between any of the pairs of the smaller objects included in the set of movable objects in parallel; and
using the distances to identify as a set of colliding objects any of the pairs of the smaller objects that are to collide with one another.
28 . The system of claim 15 , wherein the one or more circuits are to modify a particular one of the plurality of seed trajectories by performing one or more iterations until at least one stopping condition is satisfied, each of the one or more iterations comprising performing at least one optimization on the particular seed trajectory, the at least one optimization comprising:
generating a plurality of data structures representing links, at least a portion of the links being movable with respect to one another; and
performing a plurality of kinematic processes in parallel, the plurality of kinematic processes comprising at least one of a plurality of forward kinematic processes or a plurality of backward kinematic processes, the plurality of forward kinematic processes to use the plurality of data structures to obtain locations of virtual objects representing the links, the plurality of backward kinematic processes to use the plurality of data structures to obtain gradients for the virtual objects.
29 . At least one parallel processing unit (“PPU”) comprising:
one or more circuits to perform instructions that when performed by the at least one PPU cause the at least one PPU to:
generate a plurality of seed trajectories in parallel based at least in part on an initial joint configuration and a plurality of seed joint configurations that would position at least a portion of a first manipulator in a goal pose,
calculate cost values for a plurality of modified trajectories obtained by modifying the plurality of seed trajectories in parallel, and
provide a motion plan based at least in part on the cost values to a second manipulator to cause the second manipulator to move in accordance with the motion plan.
30 . The at least one PPU of claim 29 , wherein the instructions when performed by the at least one PPU cause the at least one PPU to modify a particular one of the plurality of seed trajectories by performing one or more iterations until at least one stopping condition is satisfied, each of the one or more iterations comprising performing at least one optimization on the particular seed trajectory.