Online Optimization-based Gait Adaptation of Quadruped Robot Locomotion

Quadruped robots demonstrated extensive capabilities of traversing complex and unstructured environments. Optimization-based techniques gave a relevant impulse to the research on legged locomotion. Indeed, by designing the cost function and the constraints, we can guarantee the feasibility of a motion and impose high-level locomotion tasks, e.g., tracking of a reference velocity. This allows one to have a generic planning approach without the need to tailor a specific motion for each terrain, as in the heuristic case. In this context, Model Predictive Control (MPC) can compensate for model inaccuracies and external disturbances, thanks to the high-frequency replanning. The main objective of this dissertation is to develop a Nonlinear MPC (NMPC)-based locomotion framework for quadruped robots. The aim is to obtain an algorithm which can be extended to different robots and gaits; in addition, I sought to remove some assumptions generally done in the literature, e.g., heuristic reference generator and user-defined gait sequence. The starting point of my work is the definition of the Optimal Control Problem to generate feasible trajectories for the Center of Mass. It is descriptive enough to capture the linear and angular dynamics of the robot as a whole. A simplified model (Single Rigid Body Dynamics model) is used for the system dynamics, while a novel cost term maximizes leg mobility to improve robustness in the presence of nonflat terrain. In addition, to test the approach on the real robot, I dedicated particular effort to implementing both a heuristic reference generator and an interface for the controller, and integrating them into the controller framework developed previously by other team members. As a second contribution of my work, I extended the locomotion framework to deal with a trot gait. In particular, I generalized the reference generator to be based on optimization. Exploiting the Linear Inverted Pendulum model, this new module can deal with the underactuation of the trot when only two legs are in contact with the ground, endowing the NMPC with physically informed reference trajectories to be tracked. In addition, the reference velocities are used to correct the heuristic footholds, obtaining contact locations coherent with the motion of the base, even though they are not directly optimized. The model used by the NMPC receives as input the gait sequence, thus with the last part of my work I developed an online multi-contact planner and integrated it into the MPC framework. Using a machine learning approach, the planner computes the best feasible option, even in complex environments, in a few milliseconds, by ranking online a set of discrete options for footholds, i.e., which leg to move and where to step. To train the network, I designed a novel function, evaluated offline, which considers the value of the cost of the NMPC and robustness/stability metrics for each option. These methods have been validated with simulations and experiments over the three years. I tested the NMPC on the Hydraulically actuated Quadruped robot (HyQ) of the IIT’s Dynamic Legged Systems lab, performing omni-directional motions on flat terrain and stepping on a pallet (both static and relocated during the motion) with a crawl gait. The trajectory replanning is performed at high-frequency, and visual information of the terrain is included to traverse uneven terrain. A Unitree Aliengo quadruped robot is used to execute experiments with the trot gait. The optimization-based reference generator allows the robot to reach a fixed goal and recover from external pushes without modifying the structure of the NMPC. Finally, simulations with the Solo robot are performed to validate the neural network-based contact planning. The robot successfully traverses complex scenarios, e.g., stepping stones, with both walk and trot gaits, choosing the footholds online. The achieved results improved the robustness and the performance of the quadruped locomotion. High-frequency replanning, dealing with a fixed goal, recovering after a push, and the automatic selection of footholds could help the robots to accomplish important tasks for the humans, for example, providing support in a disaster response scenario or inspecting an unknown environment. In the future, the contact planning will be transferred to the real hardware. Possible developments foresee the optimization of the gait timings, i.e., stance and swing duration, and a framework which allows the automatic transition between gaits.