Obtaining the gear stiffness of a robot joint gear of a robot arm

A method of obtaining a stiffness of a gear of a joint on a robotic arm, where the joint is connectable to at least one other joint on the robotic arm, where the joint comprises a motor having a motor axle, where the motor axle is configured to rotate an output axle through the gear, and where the method comprises:

• applying torque to the motor axle using the motor;
• obtaining an angular position of the motor axle;
• obtaining an angular position of the output axle;
• obtaining a deflection of the gear based on the angular position of the motor axle and the angular position of the output axle;
• obtaining a flexibility torque of the gear at the deflection of the gear based on at least the angular position of the motor axle, the angular position of the output axle, and a dynamic model, where the dynamic model defines a relationship between forces acting on the robotic arm and resulting accelerations of the robotic arm;
• performing operations repetitively, the operations comprising:
• applying a new torque to the motor axle using the motor;
• obtaining a new angular position of the motor axle;
• obtaining a new angular position of the output axle;
• obtaining a new deflection of the gear based on the new angular position of the motor axle and the new angular position of the output axle;
• and
• obtaining a new flexibility torque of the gear at the new deflection of the gear based on at least the new angular position of the motor axle, the new angular position of the output axle, and the dynamic model;
• storing each deflection of the gear and each flexibility torque of the gear at a corresponding deflection of the gear;
• fitting, to a mathematical function, the flexibility torques and the deflections of the gear that were stored;
• and
• determining the stiffness of the gear is based on a slope of flexibility torque relative to the deflection of the gear, the slope being based on the mathematical function.

A method of obtaining a stiffness of a gear of a joint on a robotic arm, where the joint is connectable to at least one other joint on the robotic arm, where the joint comprises a motor having a motor axle, where the motor axle is configured to rotate an output axle through the gear, and where the method comprises:

• applying torque to the motor axle using the motor, where applying the torque to the motor axle results in rotation of the motor axle and the output axle;
• obtaining an angular position of the motor axle;
• obtaining an angular position of the output axle;
• obtaining a deflection of the gear based on the angular position of the motor axle and the angular position of the output axle;
• obtaining a flexibility torque of the gear at the deflection of the gear based on at least the angular position of the motor axle, the angular position of the output axle, and a dynamic model, where the dynamic model defines a relationship between forces acting on the robotic arm and resulting accelerations of the robotic arm;
• fitting, to a mathematical function, the flexibility torque and the deflection of the gear that were obtained, where the mathematical function comprises a polynomial function that is based on a recursive least squares estimation;
• and
• determining the stiffness of the gear is based on a slope that is based on the mathematical function.