A Simplified Neural-Network Solution through Problem Decomposition: The Case of the Truck Backer-Upper

Nguyen and Widrow (1990) demonstrated that a feedforward neural network could be trained to steer a tractor-trailer truck to a dock while backing up. The feedforward network they used to control the truck contained 25 hidden units and required tens of thousands of training examples. The training strategy was to slowly expand the region in which the controller could operate, by starting with positions close to the dock and after a few thousand iterations moving the truck a little farther away. We found that a very simple solution exists requiring only two hidden units in the controller. The solution was found by decomposing the problem into subtasks. The original goal was to use the solution to these subtasks to reduce training time. What we found was a complete solution. Nevertheless, this example demonstrates how building prior knowledge into the network can dramatically simplify the problem. The problem is composed of three subtasks. First, the truck must be oriented so that the trailer is nearly normal to the dock. This is accomplished by continuously driving Ltrailer to zero by tilting the cab in the proper direction. Then, having gotten itrailer to zero or near zero, the cab must be straightened out to keep it there. Thus a restoring spring constant on Ltrailer is needed to drive Ltrailer to 0, and a restoring spring constant on icab is needed to straighten out the cab as Ltrailer approaches 0. This subnetwork depends upon the values of itrailer and Lcab and is independent of position. Once the truck is correctly oriented, the remaining objective is to dock at Y = 0. An acceptable solution is found to be independent of X, as long as the truck is not started too close to the left edge. An X dependence could be introduced to amplify the movement to Y = 0 when the truck is closer to the dock. This X dependence is equivalent to turning up the gain on the transfer function, and would best be captured by a multiplicative control term (X times Y) using 0-T units. The truck and the controller are shown in Figure 1. The specific weights used were adjusted based on observed performance, balancing between sensitivity and damping. This controller was able to successfully