In all experiments, the robot was located inside a circle of obstacles. First, the robot collected training data by randomly choosing wheel velocities and taking images through his omni-directional camera in intervals of two seconds. Then, each image was processed to obtain a lower-dimensional sensory representation. On two successive sensory representations and corresponding wheel velocities, a forward model was acquired either by using an MLP or by using the abstract RNN (chapter 4).
A single forward model can predict the future sensory input St+1 after a two second interval given the current sensory input St and the current wheel velocities Mt. In a chain of forward models, the sensory output at link t is feed into the sensory input at link t + 1. Thus, the chain can anticipate the sensory consequence of a series of motor commands.
In a first test, the anticipation performance was evaluated on a separate test set that contains random movement sequences. The changes in prediction error with an increasing number of prediction steps are analyzed for the multi-layer perceptron, the abstract RNN, and compared to a theory of the error accumulation (appendix C.3).
In the first task, the forward-model chain was applied to find a series of velocity commands that makes the robot reach a goal state. The goal state was defined within the sensory domain. The difference between the goal state and the final predicted sensory state defined a cost function. By minimizing this cost function, using either simulated annealing or Powell's method (Press et al., 1993), an appropriate series of velocities was found.
In the second task, the robot had to detect whether it was standing in the center of the circle or not. The robot could solve this task by simulating a turn around its rotational axis and by predicting the resulting sensory input. Because of the match between the robot's rotational axis and the symmetry axis of the world, the invariance in time of the predicted sensory state reflects the spatial invariance in the world.
In the third task, the robot had to judge the relative distance to obstacles, despite the non-linear mapping from the world to the camera image. This was also achieved by mental transformation. Here, a forward movement was simulated. The number of simulated movement intervals that were needed to reach the obstacle in front was counted. This number served as an estimate of the relative distance to an obstacle. Thus, the robot can perceive the real geometric relations, which are a priori not accessible to a pure sensory representation. Mallot et al. (1992, p. 16) also mentioned the possibility that distance can be perceived as `time-to-contact'.