Robust and Efficient Phase Estimation in Legged Robots via Signal Imaging and Deep Neural Networks

Accurate phase estimation in legged robots, determining whether legs are swinging or in ground contact, is crucial for stability and performance, especially on uneven terrain and with dynamic obstacles. This paper presents a novel approach to phase estimation using signal imaging and lightweight deep neural networks. Time-series data from an inertial measurement unit (IMU) and joint encoders are fused into phase images in real-time using Stacked Channels Image (SCI) and Recurrence Plot (RP) encoding methods. These phase images are then processed for phase classification, eliminating the need for force measurement sensors, which are prone to noise and failure. Extensive experiments on a 3-DoF hopping robot leg, with contact sensor data as ground truth, show that EfficientNet-B0 deep model achieves 98.97% accuracy with RP imaging and an optimized inference time of 2 milliseconds. Comparative validation on an independent dataset from the MIT Mini Cheetah traversing eight terrains demonstrates our model’s generalizability. The EfficientNet-RP-Mode1 configuration achieves 96.51% accuracy, outperforming traditional model-based methods and matching or surpassing other deep learning-based approaches, despite requiring fewer sensor inputs. This research highlights the efficiency, robustness, and adaptability of the proposed method, offering a reliable solution for phase estimation in diverse robotic platforms and environments.