Justifying operational decisions for robots is a challenging task as the operator or the robot itself has to understand the underlying physical interaction between the robot and the environment to predict the potential outcome. It is desirable to understand how the decision influences the operational performance in the way of causal relationship for the purpose of explainable decision-making. Here we propose a novel causal inference framework for the discovery and inference on the reasoning of the operational decisions for robots. It unifies both domain knowledge integration and model-free causal inference, allowing a data-driven causal knowledge learning on time series data. The framework is evaluated in the experiments of an underwater robot with complex environmental interactions. The results show that the framework can learn the causal structure and inference model to accurately explain and predict the operation performance with integrated physics.

We present a hybrid radial basis function (RBF) sigmoid neural network with a three-step training algorithm that utilizes both global search and gradient descent training. The algorithm used is intended to identify global features of an input-output relationship before adding local detail to the approximating function. It aims to achieve efficient function approximation through the separate identification of aspects of a relationship that are expressed universally from those that vary only within particular regions of the input space. We test the effectiveness of our method using five regression tasks; four use synthetic datasets while the last problem uses real-world data on the wave overtopping of seawalls. It is shown that the hybrid architecture is often superior to architectures containing neurons of a single type in several ways: lower mean square errors are often achievable using fewer hidden neurons and with less need for regularization. Our global-local artificial neural network (GL-ANN) is also seen to compare favorably with both perceptron radial basis net and regression tree derived RBFs. A number of issues concerning the training of GL-ANNs are discussed: the use of regularization, the inclusion of a gradient descent optimization step, the choice of RBF spreads, model selection, and the development of appropriate stopping criteria.