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

ContactNet: Online Multi-Contact Planning for Acyclic Legged Robot Locomotion

Online trajectory optimization techniques generally depend on heuristic-based contact planners in order to have low computation times and achieve high replanning frequencies. In this work, we propose ContactNet, a fast acyclic contact planner based on a multi-output regression neural network. ContactNet ranks discretized stepping regions, allowing to quickly choose the best feasible solution, even in complex environments. The low computation time, in the order of 1 ms, makes possible the execution of the contact planner concurrently with a trajectory optimizer in a Model Predictive Control (MPC) fashion. We demonstrate the effectiveness of the approach in simulation in different complex scenarios with the quadruped robot Solo12

Model Predictive Control With Environment Adaptation for Legged Locomotion

Re-planning in legged locomotion is crucial to track the desired user velocity while adapting to the terrain and rejecting external disturbances. In this work, we propose and test in experiments a real-time Nonlinear Model Predictive Control (NMPC) tailored to a legged robot for achieving dynamic locomotion on a variety of terrains. We introduce a mobility-based criterion to define an NMPC cost that enhances the locomotion of quadruped robots while maximizing leg mobility and improves adaptation to the terrain features. Our NMPC is based on the real-time iteration scheme that allows us to re-plan online at $25\,\mathrm{Hz}$ with a prediction horizon of $2$ seconds. We use the single rigid body dynamic model defined in the center of mass frame in order to increase the computational efficiency. In simulations, the NMPC is tested to traverse a set of pallets of different sizes, to walk into a V-shaped chimney,and to locomote over rough terrain. In real experiments, we demonstrate the effectiveness of our NMPC with the mobility feature that allowed IIT's $87\, \mathrm{kg}$ quadruped robot HyQ to achieve an omni-directional walk on flat terrain, to traverse a static pallet, and to adapt to a repositioned pallet during a walk.Comment: Video available on: https://youtu.be/r0-KIiw0eW

On the Hardware Feasibility of Nonlinear Trajectory Optimization for Legged Locomotion based on a Simplified Dynamics

Simplified models are useful to increase the computational efficiency of a motion planning algorithm, but their lack of accuracy have to be managed. We propose two feasibility constraints to be included in a Single Rigid Body Dynamicsbased trajectory optimizer in order to obtain robust motions in challenging terrain. The first one finds an approximate relationship between joint-torque limits and admissible contact forces, without requiring the joint positions. The second one proposes a leg model to prevent leg collision with the environment. Such constraints have been included in a simplified nonlinear nonconvex trajectory optimization problem. We demonstrate the feasibility of the resulting motion plans both in simulation and on the Hydraulically actuated Quadruped (HyQ) robot, considering experiments on an irregular terrain

Optimization-Based Reference Generator for Nonlinear Model Predictive Control of Legged Robots

Model predictive control (MPC) approaches are widely used in robotics, because they guarantee feasibility and allow the computation of updated trajectories while the robot is moving. They generally require heuristic references for the tracking terms and proper tuning of the parameters of the cost function in order to obtain good performance. For instance, when a legged robot has to react to disturbances from the environment (e.g., to recover after a push) or track a specific goal with statically unstable gaits, the effectiveness of the algorithm can degrade. In this work, we propose a novel optimization-based reference generator which exploits a linear inverted pendulum (LIP) model to compute reference trajectories for the center of mass while taking into account the possible underactuation of a gait (e.g., in a trot). The obtained trajectories are used as references for the cost function of the nonlinear MPC presented in our previous work. We also present a formulation that ensures guarantees on the response time to reach a goal without the need to tune the weights of the cost terms. In addition, footholds are corrected by using the optimized reference to drive the robot toward the goal. We demonstrate the effectiveness of our approach both in simulations and experiments in different scenarios with the Aliengo robot

Optimization-Based Reference Generator for Nonlinear Model Predictive Control of Legged Robots

Model predictive control (MPC) approaches are widely used in robotics, because they guarantee feasibility and allow the computation of updated trajectories while the robot is moving. They generally require heuristic references for the tracking terms and proper tuning of the parameters of the cost function in order to obtain good performance. For instance, when a legged robot has to react to disturbances from the environment (e.g., to recover after a push) or track a specific goal with statically unstable gaits, the effectiveness of the algorithm can degrade. In this work, we propose a novel optimization-based reference generator which exploits a linear inverted pendulum (LIP) model to compute reference trajectories for the center of mass while taking into account the possible underactuation of a gait (e.g., in a trot). The obtained trajectories are used as references for the cost function of the nonlinear MPC presented in our previous work. We also present a formulation that ensures guarantees on the response time to reach a goal without the need to tune the weights of the cost terms. In addition, footholds are corrected by using the optimized reference to drive the robot toward the goal. We demonstrate the effectiveness of our approach both in simulations and experiments in different scenarios with the Aliengo robot

Foothold Evaluation Criterion for Dynamic Transition Feasibility for Quadruped Robots

To traverse complex scenarios reliably a legged robot needs to move its base aided by the ground reaction forces, which can only be generated by the legs that are momentarily in contact with the ground. A proper selection of footholds is crucial for maintaining balance. In this paper, we propose a foothold evaluation criterion that considers the transition feasibility for both linear and angular dynamics to overcome complex scenarios. We devise convex and nonlinear formulations as a direct extension of [1] in a receding-horizon fashion to grant dynamic feasibility for future behaviours. The criterion is integrated with a Vision-based Foothold Adaptation (VFA) strategy that takes into account the robot kinematics, leg collisions and terrain morphology. We verify the validity of the selected footholds and the generated trajectories in simulation and experiments with the 90kg quadruped robot Hy