Continuity of Varying-Feature-Set Control Laws

Nicolas Mansard (1) , A. Remazeilles (2) , François Chaumette (3)

1 IS AIST - Intelligent Systems Institute [Tsukuba]
2 LIST (CEA) - Laboratoire d'Intégration des Systèmes et des Technologies
3 Lagadic - Visual servoing in robotics, computer vision, and augmented reality

Classical sensor-based control laws are based on the regulation of a set of sensor-based features to a desired reference value. The feature set is generally constant. In this article, we focus on the study of sensor-based control laws whose feature set varies during the servo. In that case, we first show that the classical control laws that use an iterative least-square minimization are discontinuous, and cannot be applied to real robots. We then show that these discontinuities are due to the pseudo-inverse operator, which is not continuous at matrix rank change. To solve this problem, we propose a new inversion operator. This operator is equal to the classical pseudo-inverse operator in the continuous cases, and ensures the continuity everywhere. This operator is then used to build a new control law. This general control scheme is applied to visual servoing, to ensure the continuity when some visual features leave the camera field of view. The experiments prove the interest and the validity of our approach.

Mots clés: Sensor-based control; velocity control; continuity; linear algebra; pseudo inverse; visual servoing; visibility constraint

Domaines: Robotique [cs.RO]

Nicolas Mansard, A. Remazeilles, François Chaumette. Continuity of Varying-Feature-Set Control Laws. [Research Report] PI 1864, 2007, pp.74. ⟨inria-00173777⟩