The challenge of navigating uneven terrain is a critical obstacle in the advancement of robotic
locomotion. Traditional quadrupedal locomotion methods, such as walking, are often
insufficient for dynamic and complex environments. Agile skills like jumping are necessary and
must be adaptable over uneven terrain. This study addresses this issue by developing a policy
for executing jumps over uneven terrain using a single demonstration. Initially, the system
learns to imitate a forward jump based on a single demonstration from a SLIP trajectory
planner. It then generalizes its jumping abilities to various distances in both forward and lateral
directions. The study compares the performance of systems with and without parallel elasticity,
demonstrating the energetic benefits of using elastic actuation for quadrupedal jumping.
Results show that the system with parallel elastic actuation is 15.20% more energy-efficient
and experiences a 15.79% reduction in peak power compared to the system without parallel
elasticity. A policy trained using the proposed methodology successfully performs jumps of
variable distances over uneven terrain with height perturbations of +/-4 cm using only
proprioceptive information.

In this thesis, we introduce a novel approach aimed at enhancing the jumping and landing capabilities of quadruped robots. Our method integrates both model-based and model-free strategies and features a behavioral cloning framework designed to reduce computational delays often encountered in trajectory optimization.

Initially, we build upon an existing framework for quadruped jumps, where we refine the trajectory optimization (TO) algorithm and introduce a new Variable Impedance Control (VIC). The VIC is specifically developed to facilitate softer landings. This improved system was then utilized to generate a comprehensive synthetic dataset, including 11,000 samples that cover a diverse range of jumping scenarios. This dataset served as the foundation for training a neural network. The primary objective of the network is to emulate the performance of the model-based approach. Structurally, the network is designed to process the robot's current state as input and generate the corresponding control actions for its 12 motors as output.

The most significant achievement of this research is the neural network's ability to closely replicate the outcomes of the model-based solution. Notably, it ensures more compliant behavior and lower stress on the motors during the landing phase than an MPC. The neural network demonstrates a 97.4% success rate. This high level of performance underscores its potential for on-the-fly application in robotic systems. The effectiveness of our method is further validated through a series of simulations and practical tests conducted on a Go1 quadruped robot.

Legged animals possess extraordinary agility with which they can gracefully traverse a wide range of environments, from running through grasslands to jumping across cliffs and climbing nearly vertical walls. Inspired by this, in this work, we use Deep Reinforcement Learning to give legged robots the ability to perform a diverse set of highly explosive and agile jumps. Unlike other works, our approach is not constrained to imitating a reference trajectory. We instead use curriculum-based learning to progressively learn more challenging tasks, starting from a vertical high jump and then generalising to forward and diagonal jumps. In the final curriculum stage, the robot learns to leap over barrier-like obstacles or to land on them, conditioned on the desired jumping distance and the object's dimensions. We show that such an approach can produce a wide range of robust and precise motions, which we thoroughly and successfully validated in several indoor and outdoor real-world experiments on the Unitree Go1 robot. In our real-world experiments, we show a forward jump of 90cm, exceeding previous records for similar robots reported in the literature. Additionally, we investigate the effects of incorporating bio-inspired parallel elastic actuators to improve the jumping performance further. This resulted in smoother motions, much softer landings with lower joint velocities and larger jumps. Finally, we present and analyse the limitations of our method and introduce exciting directions for future work to address them.