Augmenting Loss Functions of Feedforward Neural Networks with Differential Relationships for Robot Kinematic Modelling

Model learning is a crucial aspect of robotics as it enables the use of traditional and consolidated model-based controllers to perform desired motion tasks. However, due to the increasing complexity of robotic structures, modelling robots is becoming more and more challenging, and analytical models are very difficult to build, particularly for redundant robots. Machine learning approaches have shown great capabilities in learning complex mapping and have widely been used in robot model learning and control. Generally, inverse kinematics is learned, directly obtaining the desired control commands given a desired task. However, learning forward kinematics is simpler and allows the computation of the robot Jacobian and enables the exploitation of the optimality of controllers. Nevertheless, typical learning methods have no knowledge about the differential relationship between the position and velocity mappings. In this work, we present two novel loss functions to train feedforward Artificial Neural network (ANN) which incorporate this information in learning the forward kinematic model of robotic structures, and carry out a comparison with standard ANN training using position data only. Simulation results show that incorporating the knowledge of the velocity mapping improves the suitability of the learnt model for control tasks.