Reachable manifold and inverse mapping training for robots

A system to control movement of an end effector of a robot, the system comprising:

• a latent variable computation module configured to, based on a reachable manifold and a specified end effector pose, determine a computed latent variable that is a first intermediate variable between a set of computed robot joint angles and the specified end effector pose;
• and
• a trained inverse network module configured to, based on the specified end effector pose and the computed latent variable, determine the set of computed robot joint angles;
• wherein computed joint probabilities define the reachable manifold of the end effector of the robot;
• and wherein the reachable manifold defines whether the set of computed robot joint angles is kinematically feasible for reaching the specified end effector pose.

A system to control movement of an end effector of a robot, the system comprising:

• a control module configured to determine feasibility of a specified end effector pose of the robot when density p(x) or p(x,z) determined using a reachable manifold is greater than a reachability density threshold;
• wherein the reachable manifold defines whether a set of robot joint angles is kinematically feasible for reaching the specified end effector pose,
• wherein the reachable manifold is determined with a training system comprising:
• a first forward network module configured to, based on a set of target robot joint angles, generate a first estimated end effector pose and a first estimated latent variable that is a first intermediate variable between the set of target robot joint angles and the first estimated end effector pose;
• an inverse network module configured to determine a set of estimated robot joint angles based on (a) the first estimated latent variable and (b) a target end effector pose;
• a density network module configured to determine joint probabilities for the robot based on (a) the first estimated latent variable and (b) the target end effector pose;
• and
• a second forward network module configured to, based on the set of estimated robot joint angles, determine (a) a second estimated end effector pose and (b) a second estimated latent variable that is a second intermediate variable between the set of estimated robot joint angles and the second estimated end effector pose,
• wherein the joint probabilities define the reachable manifold of the end effector of the robot.

A method of training a neural network to control movement of an end effector of a robot, the method comprising:

• based on a set of target robot joint angles, generating a first estimated end effector pose and a first estimated latent variable that is a first intermediate variable between the set of target robot joint angles and the first estimated end effector pose;
• determining a set of estimated robot joint angles based on (a) the first estimated latent variable and (b) a target end effector pose;
• determining joint probabilities for the robot based on (a) the first estimated latent variable and (b) the target end effector pose;
• and
• based on the set of estimated robot joint angles, determining (a) a second estimated end effector pose and (b) a second estimated latent variable that is a second intermediate variable between the set of estimated robot joint angles and the second estimated end effector pose,
• wherein the joint probabilities define a reachable manifold of the end effector of the robot, and
• wherein the reachable manifold defines whether a set of robot joint angles is kinematically feasible for reaching an end effector pose.

A method of controlling movement of an end effector of a robot, the method comprising:

• based on a reachable manifold and a specified end effector pose, determining a computed latent variable that is a first intermediate variable between a set of computed robot joint angles and the specified end effector pose;
• and
• based on the specified end effector pose and the computed latent variable, determining the set of computed robot joint angles,
• wherein computed joint probabilities define the reachable manifold of the end effector of the robot, and
• wherein the reachable manifold defines whether the set of computed robot joint angles is kinematically feasible for reaching the specified end effector pose.

A method of controlling movement of an end effector of a robot, the method comprising:

• determining feasibility of a specified end effector pose of the robot when density p(x) or p(x,z) determined using a reachable manifold is greater than a reachability density threshold,
• wherein the reachable manifold defines whether a set of robot joint angles is kinematically feasible for reaching the specified end effector pose, and
• wherein the reachable manifold is determined via training including:
• based on a set of target robot joint angles, generating a first estimated end effector pose and a first estimated latent variable that is a first intermediate variable between the set of target robot joint angles and the first estimated end effector pose;
• determining a set of estimated robot joint angles based on (a) the first estimated latent variable and (b) a target end effector pose;
• determining joint probabilities for the robot based on (a) the first estimated latent variable and (b) the target end effector pose;
• and
• based on the set of estimated robot joint angles, determining (a) a second estimated end effector pose and (b) a second estimated latent variable that is a second intermediate variable between the set of estimated robot joint angles and the second estimated end effector pose,
• wherein the joint probabilities define the reachable manifold of the end effector of the robot.