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To promote the research in compliant quadrupedal locomotion, especially with parallel elasticity, we present Delft E-Go, which is an easily accessible quadruped that combines the Unitree Go1 with open-source mechanical add-ons and control architecture. Implementing this novel system required a combination of technical work and scientific innovation. First, a dedicated parallel spring with adjustable rest length is designed to strengthen each actuated joint. Then, a novel 3-D dual spring-loaded inverted pendulum model is proposed to characterize the compliant locomotion dynamics, decoupling the actuation with parallel compliance. Based on this template model, trajectory optimization is employed to generate optimal explosive motion without requiring reference defined in advance. To complete the system, a torque controller with anticipatory compensation is adopted for motion tracking. Extensive hardware experiments in multiple scenarios, such as trotting across uneven terrains, efficient walking, and explosive pronking, demonstrate the system's reliability, energy benefits of parallel compliance, and enhanced locomotion capability. Particularly, we demonstrate for the first time the controlled pronking of a quadruped with asymmetric legs.

The usage of parallel elastic actuators (PEA) in legged robots could potentially enhance the joints and increase energy efficiency by providing extra torques. However, the current design that adopts tension springs or spiral springs usually requires additional working space for PEA add-ons and enlarges size and mass too much. Besides, they often tune the spring parameters especially the spring constant by hand, failing to achieve optimal performance when considering multiple objectives. To tackle these issues, this article designs a compact dual-slide PEA (DS-PEA) leg that adopts a compression spring structure. Through integrating with a dual-slide mechanism, the PEA elements are attached tightly to the transmission, resulting in a small-size and light-weighted design. Furthermore, we adopt a multiobjective optimization method, i.e., multi-Pareto fronts quantify, to automatically choose the proper spring constant. Simulation and hardware experiments demonstrate that peak torque, motor power, and cost of transport for motion tracking are all largely reduced, even when working at multiple trajectories. Extensive hopping experiments further validate the dynamic motion capability and the energy efficiency of the delicate design. The compact DS-PEA leg will be used in a quadruped robot shortly.

Bipedal locomotion has been widely studied in recent years, where passive safety (i.e., a biped rapidly brakes without falling) is deemed to be a pivotal problem. To realize safe 3-D walking, existing works resort to nonlinear optimization techniques based on simplified dynamics models, requiring hand-tuned reference trajectories. In this article, we propose to integrate safety constraints into constrained task-space imitation learning, endowing a humanoid robot with adaptive walking capability. Specifically, unlike previous work using nonlinear and coupled capturability dynamics, we first linearize the 3-D capture conditions using appropriate extreme values and then seamlessly incorporate them into constrained imitation learning. Furthermore, we propose novel heuristic rules to define control points, enabling adaptive locomotion learning. The resulting framework allows robots to learn locomotion skills from a few demonstrations efficiently and apply the learned skills to unseen 3-D scenarios while satisfying the constraints for passive safety. Unlike deep enforcement learning, our framework avoids the need of a large number of iterations or sim-to-real transfer. By virtue of the task-space adaptability, the proposed imitation learning framework can reuse collected demonstrations in a new robot platform. We validate our method by hardware experiments on Walker2 robot and simulations on COMAN robot.