Robot Perception and Handling Actions Using the Conformal Geometric Algebra Framework

Abstract.

This paper uses an advanced geometric language for the development of theory, concepts, and computer algorithms in the domain of robot vision. Traditionally researchers use Gibb’s vector calculus, matrix algebra, tensor calculus or quaternions. In this article, the authors utilize a modern mathematical language called conformal geometric algebra, which has two main virtues: i) it can handle the representation and operations using homogeneous coordinates and ii) the necessary mathematical resources for the computation of kinematics. All the necessary computations can be done in this new framework without leaving it for certain computations. In order to show the power of this flexible mathematical language, we chose a perceptionaction system and a number of real robot-manipulation tasks to show how we model, represent, and develop real time algorithms. This paper shows how to obtain a feasible grasping strategy based on the mathematical model of the object and that of the manipulator. The 3D poses of an object and the robot hand are estimated in order to close the loop between perception, approaching, and action. In this regard, a control law with visual feedback to grasp objects is also designed using the mechanical and visual Jacobian matrix in terms of the line axis of the Barrett hand and the principal optical planes of the camera. The authors want to draw the attention of the community to a promising geometric language for robot vision.