2 Differential visual feedback



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Next: 2.1 Derivation of a Up: Adaptive DVFB for Uncal. Previous: 1 Introduction

2 Differential visual feedback

This section describes the differential visual feedback controller we use, and issues relevant to its design.

  
Figure 1: Typical visual control setup uses two cameras placed so that they can observe the workspace from two different viewpoints. Otherwise, placement is arbitrary, and the controller has no prior knowledge of the camera locations, their relation to the robot, or the robot kinematics. The setpoints for the robot joint angles are specified by the vector , and visual perceptions, or features are represented by the vector , These are related by an initially unknown transfer function .

The situation depicted in fig. 1 shows a typical setup for visual servoing. For three and higher DOF control we typically want to use at least two cameras, spaced widely enough apart to give well conditioned depth cues. Otherwise, camera placement is fairly arbitrary. In the images taken by the cameras we extract, and continuously track, the positions of interesting features, for instance, the position of the robot end effector. We denote the vector of visual features by . gif Features suitable for visual control can be drawn from a much wider class of measurements in the image, and we will discuss this later. However, for the purposes of the derivations in this section, thinking of the visual features as image the location of tracked features will suffice.

The vector x, represents the output signals from the controller. In this example, for conceptual simplicity, we let x be robot joint positions. In our actual implementation we will use a combination of position and velocity control.

In a traditional visual control setup we have to know two functions, either a-priori, or through some calibration process. The first is a camera, or vision calibration function that transforms image space feature locations to a Cartesian world coordinate system (typically having its origin at the base of the robot). The second is the robot kinematic calibration function that transforms desired robot end effector positions, given in world coordinates, into joint angles. The final robot positioning accuracy depends on the accuracy of both these functions (), since feedback is only performed over the joint values.

It was realized early on that accuracy could be improved by using residual visual error, measured after a movement was executed, to perform a correction move. [Weiss 84] classified such schemes as Position based (iterated) look-and-move approaches. The next step was to notice that if goal points were provided in image coordinates and realized through joint angles, then the intermediate world coordinate system could be completely eliminated. Weiss calls this Image based look-and-move. Finally, if instead of supplying visual error only occasionally, our system servos joints using a continuous visual signal, we have what Weiss calls Image based visual servoing.

We present a system which can learn a sufficing mapping from image based (vision space) specification, to robot (joint space) execution primitives. The system requires no prior models of the transfer function; it learns the model while performing the task without explicitly introducing any extra learning steps or movements. It is capable of learning multivariate (coupled, vector valued) transfer functions with an arbitrary number of visual inputs and an arbitrary number of output control signals. The method places only very loose constraints on which transfer functions can be successfully learned.





next up previous
Next: 2.1 Derivation of a Up: Adaptive DVFB for Uncal. Previous: 1 Introduction



jag@cs.rochester.edu