Gradient Projection Methods for Constrained Image-based Visual Servo - Visual Servoing via Advanced Numerical Methods - page 242

Chapter 14
Gradient Projection Methods for Constrained
Image-based Visual Servo

Wenzhuo Ma and Seth Hutchinson

Abstract. This chapter describes redundancy-based solutions to visual servo prob-
lems that require honoring constraints on camera motion that are imposed either by
the environment or by physical limits on the robot system. The task function ap-
proach provides a formalism by which a secondary task can be achieved without
disturbing the execution of the primary task. For problems considered here, sec-
ondary tasks correspond to enforcing various constraints. With gradient projection
methods, the secondary task corresponds to the gradient of a cost function, and this
gradient is projected onto the null space of the primary task to yield motions that
will honor the constraints without interfering with the performance of the primary
task. The chapter reprises the development of gradient projection methods in the
context of constrained visual servo control, and presents simulation results to illus-
trate performance of the approach.

14.1 Introduction

In this chapter we consider the problem of performing visual servo tasks while re-
specting constraints on camera motion. In particular, we consider constraints on
camera motion that derive from robot joint limits, the possibility of occlusion, and
the need to keep objects of interest in the field of view during task execution. While
there are many scenarios in which this type of constrained visual servo would be
appropriate, we limit our attention here to the case in which the visual servo system
is redundant with respect to the task ( i.e. , the camera motion has more degrees of
freedom (DOF) than are required to execute the task). In such cases, constraints can
be formulated as a secondary task, and the redundant DOF can be used to satisfy
those constraints [15, 12].