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

Bridging Vision and Dynamic Legged Locomotion

Legged robots have demonstrated remarkable advances regarding robustness and versatility in the past decades. The questions that need to be addressed in this field are increasingly focusing on reasoning about the environment and autonomy rather than locomotion only. To answer some of these questions visual information is essential. If a robot has information about the terrain it can plan and take preventive actions against potential risks. However, building a model of the terrain is often computationally costly, mainly because of the dense nature of visual data. On top of the mapping problem, robots need feasible body trajectories and contact sequences to traverse the terrain safely, which may also require heavy computations. This computational cost has limited the use of visual feedback to contexts that guarantee (quasi-) static stability, or resort to planning schemes where contact sequences and body trajectories are computed before starting to execute motions. In this thesis we propose a set of algorithms that reduces the gap between visual processing and dynamic locomotion. We use machine learning to speed up visual data processing and model predictive control to achieve locomotion robustness. In particular, we devise a novel foothold adaptation strategy that uses a map of the terrain built from on-board vision sensors. This map is sent to a foothold classifier based on a convolutional neural network that allows the robot to adjust the landing position of the feet in a fast and continuous fashion. We then use the convolutional neural network-based classifier to provide safe future contact sequences to a model predictive controller that optimizes target ground reaction forces in order to track a desired center of mass trajectory. We perform simulations and experiments on the hydraulic quadruped robots HyQ and HyQReal. For all experiments the contact sequences, the foothold adaptations, the control inputs and the map are computed and processed entirely on-board. The various tests show that the robot is able to leverage the visual terrain information to handle complex scenarios in a safe, robust and reliable manner

Keep Rollin' - Whole-Body Motion Control and Planning for Wheeled Quadrupedal Robots

We show dynamic locomotion strategies for wheeled quadrupedal robots, which combine the advantages of both walking and driving. The developed optimization framework tightly integrates the additional degrees of freedom introduced by the wheels. Our approach relies on a zero-moment point based motion optimization which continuously updates reference trajectories. The reference motions are tracked by a hierarchical whole-body controller which computes optimal generalized accelerations and contact forces by solving a sequence of prioritized tasks including the nonholonomic rolling constraints. Our approach has been tested on ANYmal, a quadrupedal robot that is fully torque-controlled including the non-steerable wheels attached to its legs. We conducted experiments on flat and inclined terrains as well as over steps, whereby we show that integrating the wheels into the motion control and planning framework results in intuitive motion trajectories, which enable more robust and dynamic locomotion compared to other wheeled-legged robots. Moreover, with a speed of 4 m/s and a reduction of the cost of transport by 83 % we prove the superiority of wheeled-legged robots compared to their legged counterparts.Comment: IEEE Robotics and Automation Letter

Motion Planning for Quadrupedal Locomotion:Coupled Planning, Terrain Mapping and Whole-Body Control

Planning whole-body motions while taking into account the terrain conditions is a challenging problem for legged robots since the terrain model might produce many local minima. Our coupled planning method uses stochastic and derivatives-free search to plan both foothold locations and horizontal motions due to the local minima produced by the terrain model. It jointly optimizes body motion, step duration and foothold selection, and it models the terrain as a cost-map. Due to the novel attitude planning method, the horizontal motion plans can be applied to various terrain conditions. The attitude planner ensures the robot stability by imposing limits to the angular acceleration. Our whole-body controller tracks compliantly trunk motions while avoiding slippage, as well as kinematic and torque limits. Despite the use of a simplified model, which is restricted to flat terrain, our approach shows remarkable capability to deal with a wide range of noncoplanar terrains. The results are validated by experimental trials and comparative evaluations in a series of terrains of progressively increasing complexity

Trajectory and Foothold Optimization using Low-Dimensional Models for Rough Terrain Locomotion

We present a trajectory optimization framework for legged locomotion on rough terrain. We jointly optimize the center of mass motion and the foothold locations, while considering terrain conditions. We use a terrain costmap to quantify the desirability of a foothold location. We increase the gait's adaptability to the terrain by optimizing the step phase duration and modulating the trunk attitude, resulting in motions with guaranteed stability. We show that the combination of parametric models, stochastic-based exploration and receding horizon planning allows us to handle the many local minima associated with different terrain conditions and walking patterns. This combination delivers robust motion plans without the need for warm-starting. Moreover, we use soft-constraints to allow for increased flexibility when searching in the cost landscape of our problem. We showcase the performance of our trajectory optimization framework on multiple terrain conditions and validate our method in realistic simulation scenarios and experimental trials on a hydraulic, torque controlled quadruped robot

Whole-body control with disturbance rejection through a momentum-based observer for quadruped robots☆

This paper presents an estimator of external disturbances for legged robots, based on the system’s momentum. The estimator, along with a suitable motion planner for the trajectory of the robot’s center of mass and an optimization problem based on the modulation of ground reaction forces, devises a whole-body controller for the robot. The designed solution is tested on a quadruped robot within a dynamic simulation environment. The quadruped is stressed by external disturbances acting on stance and swing legs indifferently. The proposed approach is also evaluated through a comparison with two state-of-the-art solutions

Model Predictive Control for Legged Robots

Optimal planning is essential when it comes to autonomy in legged locomotion. In the last few decades, different optim- ization techniques have been presented to design a legged lo- comotion framework, such as Trajectory Optimization (TO) and Model Predictive Control (MPC). The choice of a dy- namic model utilized while synthesizing these planners plays a pivotal role because the chosen model defines the accuracy of the planning and also becomes a deciding factor for the computational cost of these techniques. In the first part of this thesis, we propose a closed-loop validation procedure for the Single Rigid Body Dynamics (SRBD) model and its vari- ants used for optimal planning. Thereafter, we introduce a Linear Time-Varying (LTV) based TO for legged locomotion, followed by the simulation results and discussion on its lim- itations in re-planning. Re-planning in legged locomotion is crucial to track the de- sired user velocity while adapting to the terrain and reject- ing external disturbances. In the second part of this thesis, we propose and test in experiments a real-time Nonlinear Model Predictive Control (NMPC) tailored to a legged robot to achieve dynamic locomotion on various terrains. We in- troduce a novel mobility-based criterion to define an NMPC cost that enhances the locomotion of quadruped robots while maximizing leg mobility and improving adaptation to the ter- rain features. The NMPC is based on the Real-Time Iteration (RTI) scheme that allows us to re-plan online at 25 Hz with a prediction horizon of 2 seconds. In simulations, the NMPC is tested to traverse a set of pallets of different sizes, walk into a V-shaped chimney, and locomote over rough terrain. In real experiments, we demonstrate the effectiveness of our NMPC with the mobility feature that allowed IIT’s 87 kg quadruped robot HyQ to achieve an omni-directional walk on flat terrain, traverse a static pallet, and adapt to a repositioned pallet dur- ing a walk.In the final part of this thesis, we present the extension of the NMPC with other dynamic gaits, i.e., trot and pace. We also introduce an Optimization-Based Reference Gener- ator (ORG) that computes dynamically feasible trajectories for the state and control input based on the Linear Inver- ted Pendulum (LIP) model-based optimization and Quad- ratic Programming (QP) based mapping. These feasible tra- jectories are passed to the NMPC to cope with the disturb- ances while following the user-defined trajectories with the dynamic gaits. We show the effectiveness of this two-stage optimization scheme in simulations and experiments per- formed on the AlienGo robot to trot in a straight line and to recover from the external disturbances while trotting. We also compare the performance of the two-stage scheme with respect to a traditional heuristic reference generator in an ex- periment