Robot control at singular configurations

A computer-implemented method for controlling a robot having an endpoint and a plurality of joints providing more than three degrees of freedom (DoFs), the method comprising:

• selecting impedance parameters for each of a plurality of impedance modules, wherein each of the plurality of impedance modules specifies a robot behavior associated with a task;
• for one or more of the impedance modules:
• receiving an endpoint impedance matrix representing a desired stiffness or damping at the robot endpoint,
• reflecting the endpoint impedance matrix to an equivalent joint-space matrix associated with one or more of the robot joints, the equivalent joint-space matrix having a nullspace corresponding to near-zero-valued eigenvalues,
• generating a nullspace-filled impedance matrix from the equivalent joint-space matrix based in part on replacing the near-zero-valued eigenvalues with selected finite positive real values, wherein the replacing of the near-zero-valued eigenvalues with the selected finite positive real values includes, in response to detecting that the robot is approaching a kinematic singularity, increasing one or more eigenvalues from a threshold value to the corresponding selected finite positive real value, and
• defining an impedance control law for the module using the nullspace-filled stiffness matrix and the impedance parameters selected for the module;
• generating a composite control law for the robot using impedance module control laws defined for the impedance modules;
• and
• using the composite control law to control the robot.

A system comprising:

• a robot having an endpoint and a plurality of joints providing more than three degrees of freedom (DoFs);
• and
• an impedance controller configured to:
• receive an endpoint impedance matrix representing a desired stiffness or damping at the robot endpoint;
• reflect the endpoint impedance matrix to an equivalent joint-space matrix associated with one or more of the robot joints, the equivalent joint-space matrix having a nullspace corresponding to near-zero-valued eigenvalues;
• generate a nullspace-filled impedance matrix from the equivalent joint-space matrix based in part on replacing the near-zero-valued eigenvalues with selected finite positive real values, wherein the replacing of the near-zero-valued eigenvalues with the selected finite positive real values includes, in response to detecting that the robot is approaching a kinematic singularity, increasing one or more eigenvalues from a threshold value to the corresponding selected finite positive real value;
• generate a robot control law using the nullspace-filled impedance matrix;
• and
• use the robot control law to control the robot.