Dual-arm admittance control using conformal geometric algebra

We propose a task-space admittance controller for dual-arm robotic systems using conformal geometric algebra. The controller is a reinterpretation of a previous work using dual quaternion algebra. By introducing conformal geometric algebra, we aim to enhance the geometric expressiveness, which simplifies the modeling of various tasks and opens doors to more complex applications, such as the modeling of multiple points of contact on the robotic arm in a whole-body manipulation task. We first show the derivation of the controller for a single-arm robot, which is then extended to a dual-arm robot. The closed-loop system is therefore composed of an outer loop admittance controller that imposes the apparent impedance, and an inner loop that transforms the twist acceleration to a control input that is sent to the robot. Experiments executed on a setup with two LBR KUKA iiwa 14 R820 robots with a force/torque sensor in each end-effector show good performance of the proposed controller for both single and dual-arm tasks. Namely, the system was able to reach the desired poses in the absence of external wrenches, while moving in a compliant manner in the presence of external wrenches, adapting the robot's motion to keep the desired impedance.