Time delays in a HyperNEAT network to improve gait learning for legged robots

Gait generation for legged robots is an important task to allow an appropriate displacement in different scenarios. The classical manner to generate gaits involves hand-tuning design generating high computational and time efforts. Neuroevolution algorithms with the ability to learn network topologies, such as, Neuroevolution of Augmenting Topologies (NEAT) and Hypercube-based NEAT (HyperNEAT), have been used in the computational community to learn gaits in legged robots. Recently, a new version of NEAT, called τ-NEAT, has been reported including a time delay in the connectivity between neurons, values that are also learned by the underlying genetic algorithm. Extending this idea, we included time delays in the HyperNEAT implementation (τ-HyperNEAT) making the algorithm capture time-series variations that could be important for gait generation. Using a four-legged robot platform (Quadratot) and a fitness function with two objectives, we compared the performance of HyperNEAT versus τ-HyperNEAT for the learning gait task. The comparative analysis of the results reveals that quantitative performance variables showed no differences between HyperNEAT and τ-HyperNEAT. The difference between the two approaches appears in the non-quantitative observation of the generated gaits: τ-HyperNEAT outperforms HyperNEAT generating more coordinated, realistic and natural gaits.