Real time generation of phase synchronized trajectories

A method implemented by one or more processors of a robot, comprising:

• identifying, at a first time, a first target motion state of actuators of the robot;
• generating first time-optimal trajectories for the actuators, wherein each of the first time-optimal trajectories is for a corresponding one of the actuators, and wherein the first time-optimal trajectories time-optimally transfer, with respect to shortest time, a motion state of the actuators at the first time to the first target motion state of the actuators;
• generating time-optimal phase synchronized trajectories that are a time-optimal phase synchronization of the time-optimal trajectories;
• using the time-optimal phase synchronized trajectories to operate the plurality of actuators of the robot in reaching the first target motion state from the motion state of the actuators at the first time;
• identifying, at a second time, a second target motion state of the actuators of the robot;
• generating second time-optimal trajectories for the actuators, wherein each of the second time-optimal trajectories is for a corresponding one of the actuators, and wherein the second time-optimal trajectories time-optimally transfer a current motion state of the actuators at the second time to the second target motion state of the actuators;
• determining whether time-optimal phase synchronization for the second time-optimal trajectories is achievable;
• in response to determining that time-optimal phase synchronization for the second time-optimal trajectories is not achievable, generating phase synchronized trajectories for the actuators that are less time-optimal than the second time-optimal trajectories;
• and
• using the phase synchronized trajectories to operate the plurality of actuators of the robot in reaching the second target motion state from the current motion state of the actuators at the second time.

A robot comprising:

• a plurality of actuators;
• one or more processors configured to:
• identify a target motion state of the actuators of the robot;
• generate time-optimal trajectories for the plurality of actuators, wherein each of the time-optimal trajectories is for a corresponding one of the plurality of actuators, and wherein each of the time-optimal trajectories defines corresponding motion states for a corresponding one of the plurality of actuators,
• wherein the time-optimal trajectories, if implemented, time-optimally transfer a current motion state of the plurality of actuators to the target motion state of the plurality of actuators,
• wherein generating the time-optimal trajectories is based on:
• the current motion state of the plurality of actuators, the target motion state of the plurality of actuators, and kinematic motion constraints of the plurality of actuators, and
• wherein time-optimally is optimal with respect to transferring the current motion state to the target motion state in the shortest time possible;
• determine whether time-optimal phase synchronization of the time-optimal trajectories is not achievable;
• in response to determining that the time-optimal phase synchronization is not achievable, time-scale a particular time-optimal trajectory of the time optimal trajectories, to create a time-scaled trajectory, wherein the particular time-optimal trajectory is for a particular actuator of the plurality of actuators and is time-scaled based on having the largest execution time to create a time;
• determine, for each of the plurality of actuators that are in addition to the particular actuator having the particular time-optimal trajectory with the largest execution time, a phase scale factor;
• generate phase synchronized trajectories for the plurality of actuators that are in addition to the particular actuator having the time-optimal trajectory with the largest execution time, wherein a corresponding one of the phase synchronized trajectories is generated for each of the plurality of actuators that are in addition to the particular actuator having the particular time-optimal trajectory with the largest execution time, and wherein generating a phase synchronized trajectory, of the phase synchronized trajectories, for a given actuator, of the plurality of actuators that are in addition to the particular actuator, is based on phase-scaling the particular time-scaled trajectory for the given actuator based on the phase scale factor for the given actuator that is in addition to the particular actuator;
• and
• the particular actuator using the particular time-scaled trajectory and operating the plurality of actuators that are in addition to the particular actuator using the phase synchronized trajectories.