Fast Learning Mapping Schemes for Robotic Hand–Eye Coordination

Abstract

In aiming for advanced robotic systems that autonomously and permanently readapt to changing and uncertain environments, we introduce a scheme of fast learning and readaptation of robotic sensorimotor mappings based on biological mechanisms underpinning the development and maintenance of accurate human reaching. The study presents a range of experiments, using two distinct computational architectures, on both learning and realignment of robotic hand–eye coordination. Analysis of the results provide insights into the putative parameters and mechanisms required for fast readaptation and generalization from both a robotic and biological perspective.

Appendices

Appendix 1: Uncertainty of the Active Vision System

In order to evaluate these results in relation to the uncertainty of the active vision system, the average tilt–verge values for specific object locations were also derived (Table 7). One can see that the vision system has a uncertainty of ≈0.002 rad in average for tilt and verge motors. The complete vision domain, however, is approximately 0.2 rad³. Therefore, out of 2.5 × 10⁷ distinguishable samples in the vision space, our method requires only 300 examples to achieve the given performance in robotic hand–eye coordination.

Table 7 Average and standard deviation of tilt, verge left and verge right values delivered by active vision system resulting from the saccade toward an object on the table at specific positions

Appendix 2: Approximation of ${\mathcal{S}}$ in $A_{\mathcal{S}}$

The parameters for approximating the shifts in visual space via quadratic and linear regression as well as the simple mean value are summarized in Table 8. The quadratic functions provide the best match, which are plotted in Fig. 14 overlaid by the actual offset values derived from the mappings ${\mathcal{R}}_C$ and ${\mathcal{R}}_S$

Table 8 Parameters for the functions Δ (x) =  ax ² + bx + c approximating the offset in visual space

Fig. 14

Empirical data representing the offset needed to shift the points in visual space in order to compensate the change from the centered to the shifted arm–vision configuration. The three diagrams show the offsets of a component over its absolute value for tilt (top), verge left (middle) and verge right (bottom). In addition, the trend lines for the quadratic approximation are shown