Deep reinforcement learning (DRL) has emerged as a promising solution to mastering explosive and versatile quadrupedal jumping skills. However, current DRL-based frameworks usually rely on pre-existing reference trajectories obtained by capturing animal motions or transferring experience from existing controllers. This work aims to prove that learning dynamic jumping is possible without relying on imitating a reference trajectory by leveraging a curriculum design. Starting from a vertical in-place jump, we generalize the learned policy to forward and diagonal jumps and, finally, we learn to jump across obstacles. Conditioned on the desired landing location, orientation, and obstacle dimensions, the proposed approach yields a wide range of omnidirectional jumping motions in real-world experiments. In particular, we achieve a 90 cm forward jump, exceeding all previous records for similar robots. Additionally, the robot can reliably execute continuous jumping on soft grassy grounds, which is especially remarkable as such conditions were not included in the training stage.

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.

Introducing parallel elasticity in the hardware design endows quadrupedal robots with the ability to perform explosive and efficient motions. However, for this kind of articulated soft quadruped, realizing dynamic jumping with robustness against system uncertainties remains a challenging problem. To achieve this, we propose an impact-aware jumping planning and control approach. Specifically, an offline kino-dynamic-type trajectory optimizer is first formulated to achieve compliant 3D jumping motions, using a novel actuated spring-loaded inverted pendulum (SLIP) model. Then, an optimization-based online landing strategy, including pre-impact leg motion modulation and post-impact landing recovery, is designed. The actuated SLIP model, with the capability of explicitly characterizing parallel elasticity, captures the jumping and landing dynamics, making the problem of motion generation/regulation more tractable. Finally, a hybrid torque control consisting of a feedback tracking loop and a feedforward compensation loop is employed for motion control. Experiments demonstrate the ability to accomplish robust 3D jumping motions with stable landing and recovery. Besides, our approach can be applied to quadrupedal robots with or without additional parallel compliance.