Nonlinear Model Predictive Control for Motion Generation of Humanoids

Das Ziel dieser Arbeit ist die Untersuchung und Entwicklung numerischer Methoden zur Bewegungserzeugung von humanoiden Robotern basierend auf nichtlinearer modell-prädiktiver Regelung. Ausgehend von der Modellierung der Humanoiden als komplexe Mehrkörpermodelle, die sowohl durch unilaterale Kontaktbedingungen beschränkt als auch durch die Formulierung unteraktuiert sind, wird die Bewegungserzeugung als Optimalsteuerungsproblem formuliert. In dieser Arbeit werden numerische Erweiterungen basierend auf den Prinzipien der Automatischen Differentiation für rekursive Algorithmen, die eine effiziente Auswertung der dynamischen Größen der oben genannten Mehrkörperformulierung erlauben, hergeleitet, sodass sowohl die nominellen Größen als auch deren ersten Ableitungen effizient ausgewertet werden können. Basierend auf diesen Ideen werden Erweiterungen für die Auswertung der Kontaktdynamik und der Berechnung des Kontaktimpulses vorgeschlagen. Die Echtzeitfähigkeit der Berechnung von Regelantworten hängt stark von der Komplexität der für die Bewegungerzeugung gewählten Mehrkörperformulierung und der zur Verfügung stehenden Rechenleistung ab. Um einen optimalen Trade-Off zu ermöglichen, untersucht diese Arbeit einerseits die mögliche Reduktion der Mehrkörperdynamik und andererseits werden maßgeschneiderte numerische Methoden entwickelt, um die Echtzeitfähigkeit der Regelung zu realisieren. Im Rahmen dieser Arbeit werden hierfür zwei reduzierte Modelle hergeleitet: eine nichtlineare Erweiterung des linearen inversen Pendelmodells sowie eine reduzierte Modellvariante basierend auf der centroidalen Mehrkörperdynamik. Ferner wird ein Regelaufbau zur GanzkörperBewegungserzeugung vorgestellt, deren Hauptbestandteil jeweils aus einem speziell diskretisierten Problem der nichtlinearen modell-prädiktiven Regelung sowie einer maßgeschneiderter Optimierungsmethode besteht. Die Echtzeitfähigkeit des Ansatzes wird durch Experimente mit den Robotern HRP-2 und HeiCub verifiziert. Diese Arbeit schlägt eine Methode der nichtlinear modell-prädiktiven Regelung vor, die trotz der Komplexität der vollen Mehrkörperformulierung eine Berechnung der Regelungsantwort in Echtzeit ermöglicht. Dies wird durch die geschickte Kombination von linearer und nichtlinearer modell-prädiktiver Regelung auf der aktuellen beziehungsweise der letzten Linearisierung des Problems in einer parallelen Regelstrategie realisiert. Experimente mit dem humanoiden Roboter Leo zeigen, dass, im Vergleich zur nominellen Strategie, erst durch den Einsatz dieser Methode eine Bewegungserzeugung auf dem Roboter möglich ist. Neben Methoden der modell-basierten Optimalsteuerung werden auch modell-freie Methoden des verstärkenden Lernens (Reinforcement Learning) für die Bewegungserzeugung untersucht, mit dem Fokus auf den schwierig zu modellierenden Modellunsicherheiten der Roboter. Im Rahmen dieser Arbeit werden eine allgemeine vergleichende Studie sowie Leistungskennzahlen entwickelt, die es erlauben, modell-basierte und -freie Methoden quantitativ bezüglich ihres Lösungsverhaltens zu vergleichen. Die Anwendung der Studie auf ein akademisches Beispiel zeigt Unterschiede und Kompromisse sowie Break-Even-Punkte zwischen den Problemformulierungen. Diese Arbeit schlägt basierend auf dieser Grundlage zwei mögliche Kombinationen vor, deren Eigenschaften bewiesen und in Simulation untersucht werden. Außerdem wird die besser abschneidende Variante auf dem humanoiden Roboter Leo implementiert und mit einem nominellen modell-basierten Regler verglichen

From walking to running: robust and 3D humanoid gait generation via MPC

Humanoid robots are platforms that can succeed in tasks conceived for humans. From locomotion in unstructured environments, to driving cars, or working in industrial plants, these robots have a potential that is yet to be disclosed in systematic every-day-life applications. Such a perspective, however, is opposed by the need of solving complex engineering problems under the hardware and software point of view. In this thesis, we focus on the software side of the problem, and in particular on locomotion control. The operativity of a legged humanoid is subordinate to its capability of realizing a reliable locomotion. In many settings, perturbations may undermine the balance and make the robot fall. Moreover, complex and dynamic motions might be required by the context, as for instance it could be needed to start running or climbing stairs to achieve a certain location in the shortest time. We present gait generation schemes based on Model Predictive Control (MPC) that tackle both the problem of robustness and tridimensional dynamic motions. The proposed control schemes adopt the typical paradigm of centroidal MPC for reference motion generation, enforcing dynamic balance through the Zero Moment Point condition, plus a whole-body controller that maps the generated trajectories to joint commands. Each of the described predictive controllers also feature a so-called stability constraint, preventing the generation of diverging Center of Mass trajectories with respect to the Zero Moment Point. Robustness is addressed by modeling the humanoid as a Linear Inverted Pendulum and devising two types of strategies. For persistent perturbations, a way to use a disturbance observer and a technique for constraint tightening (to ensure robust constraint satisfaction) are presented. In the case of impulsive pushes instead, techniques for footstep and timing adaptation are introduced. The underlying approach is to interpret robustness as a MPC feasibility problem, thus aiming at ensuring the existence of a solution for the constrained optimization problem to be solved at each iteration in spite of the perturbations. This perspective allows to devise simple solutions to complex problems, favoring a reliable real-time implementation. For the tridimensional locomotion, on the other hand, the humanoid is modeled as a Variable Height Inverted Pendulum. Based on it, a two stage MPC is introduced with particular emphasis on the implementation of the stability constraint. The overall result is a gait generation scheme that allows the robot to overcome relatively complex environments constituted by a non-flat terrain, with also the capability of realizing running gaits. The proposed methods are validated in different settings: from conceptual simulations in Matlab to validations in the DART dynamic environment, up to experimental tests on the NAO and the OP3 platforms

Humanoid Robotic Manipulation Benchmarking and Bimanual Manipulation Workspace Analysis

The growing adoption of robots for new applications has led to the use of robots in human environments for human-like tasks, applications well-suited to humanoid robots as they are designed to move like a human and operate in similar environments. However, a user must decide which robot and control algorithm is best suited to the task, motivating the need for standardized performance comparison through benchmarking. Typical humanoid robotic scenarios in many household and industrial tasks involve manipulation of objects with two hands, bimanual manipulation. Understanding how these can be performed in the humanoid’s workspace is especially challenging due to the highly constrained nature due to grasp and stability requirements, but very important for introducing humanoid robots into human environments for human-like tasks. The first topic this thesis focuses on is benchmarking manipulation for humanoid robotics. The evaluation of humanoid manipulation can be considered for whole-body manipulation, manipulation while standing and remaining balanced, or loco-manipulation, taking steps during manipulation. As part of the EUROBENCH project, which aims to develop a unified benchmarking framework for robotic systems performing locomotion tasks, benchmarks for whole-body manipulation and loco-manipulation are proposed consisting of standardized test beds, comprehensive experimental protocols, and insightful key performance indicators. For each of these benchmarks, partial initial benchmarks are performed to begin evaluating the difference in performance of the University of Waterloo’s REEM- C, “Seven”, using two different motion generation and control strategies. These partial benchmarks showed trade-offs in speed and efficiency for placement accuracy. The second topic of interest is bimanual manipulation workspace analysis of humanoid robots. To evaluate the ability of a humanoid robot to bimanually manipulate a box while remaining balanced, a new metric for combined manipulability-stability is developed based on the volume of the manipulability ellipsoid and the distance of the capture point from the edge of the support polygon. Using this metric, visualizations of the workspace are performed for the following scenarios: when the center of mass of the humanoid has a velocity, manipulating objects of different size and mass, and manipulating objects using various grips. To examine bimanual manipulation with different fixed grasps the manipulation of two different boxes, a broom and a rolling pin are visualized to see how grip affects the feasibility and manipulability-stability quality of a task. Visualizations of REEM-C and TALOS are also performed for a general workspace and a box manipulation task to compare their workspaces as they have different kinematic structures. These visualizations provide a better understanding of how manipulability and stability are impacted in a bimanual manipulation scenario

Do robots outperform humans in human-centered domains?

The incessant progress of robotic technology and rationalization of human manpower induces high expectations in society, but also resentment and even fear. In this paper, we present a quantitative normalized comparison of performance, to shine a light onto the pressing question, "How close is the current state of humanoid robotics to outperforming humans in their typical functions (e.g., locomotion, manipulation), and their underlying structures (e.g., actuators/muscles) in human-centered domains?" This is the most comprehensive comparison of the literature so far. Most state-of-the-art robotic structures required for visual, tactile, or vestibular perception outperform human structures at the cost of slightly higher mass and volume. Electromagnetic and fluidic actuation outperform human muscles w.r.t. speed, endurance, force density, and power density, excluding components for energy storage and conversion. Artificial joints and links can compete with the human skeleton. In contrast, the comparison of locomotion functions shows that robots are trailing behind in energy efficiency, operational time, and transportation costs. Robots are capable of obstacle negotiation, object manipulation, swimming, playing soccer, or vehicle operation. Despite the impressive advances of humanoid robots in the last two decades, current robots are not yet reaching the dexterity and versatility to cope with more complex manipulation and locomotion tasks (e.g., in confined spaces). We conclude that state-of-the-art humanoid robotics is far from matching the dexterity and versatility of human beings. Despite the outperforming technical structures, robot functions are inferior to human ones, even with tethered robots that could place heavy auxiliary components off-board. The persistent advances in robotics let us anticipate the diminishing of the gap

Dynamic Walking: Toward Agile and Efficient Bipedal Robots

Dynamic walking on bipedal robots has evolved from an idea in science fiction to a practical reality. This is due to continued progress in three key areas: a mathematical understanding of locomotion, the computational ability to encode this mathematics through optimization, and the hardware capable of realizing this understanding in practice. In this context, this review article outlines the end-to-end process of methods which have proven effective in the literature for achieving dynamic walking on bipedal robots. We begin by introducing mathematical models of locomotion, from reduced order models that capture essential walking behaviors to hybrid dynamical systems that encode the full order continuous dynamics along with discrete footstrike dynamics. These models form the basis for gait generation via (nonlinear) optimization problems. Finally, models and their generated gaits merge in the context of real-time control, wherein walking behaviors are translated to hardware. The concepts presented are illustrated throughout in simulation, and experimental instantiation on multiple walking platforms are highlighted to demonstrate the ability to realize dynamic walking on bipedal robots that is agile and efficient

Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach

We introduce a real-time, constrained, nonlinear Model Predictive Control for the motion planning of legged robots. The proposed approach uses a constrained optimal control algorithm known as SLQ. We improve the efficiency of this algorithm by introducing a multi-processing scheme for estimating value function in its backward pass. This pass has been often calculated as a single process. This parallel SLQ algorithm can optimize longer time horizons without proportional increase in its computation time. Thus, our MPC algorithm can generate optimized trajectories for the next few phases of the motion within only a few milliseconds. This outperforms the state of the art by at least one order of magnitude. The performance of the approach is validated on a quadruped robot for generating dynamic gaits such as trotting.Comment: 8 page

Advanced human inspired walking strategies for humanoid robots

Cette thèse traite du problème de la locomotion des robots humanoïdes dans le contexte du projet européen KoroiBot. En s'inspirant de l'être humain, l'objectif de ce projet est l'amélioration des capacités des robots humanoïdes à se mouvoir de façon dynamique et polyvalente. Le coeur de l'approche scientifique repose sur l'utilisation du controle optimal, à la fois pour l'identification des couts optimisés par l'être humain et pour leur mise en oeuvre sur les robots des partenaires roboticiens. Cette thèse s'illustre donc par une collaboration à la fois avec des mathématiciens du contrôle et des spécialistes de la modélisation des primitives motrices. Les contributions majeures de cette thèse reposent donc sur la conception de nouveaux algorithmes temps-réel de contrôle pour la locomotion des robots humanoïdes avec nos collégues de l'université d'Heidelberg et leur intégration sur le robot HRP-2. Deux contrôleurs seront présentés, le premier permettant la locomotion multi-contacts avec une connaissance a priori des futures positions des contacts. Le deuxième étant une extension d'un travail réalisé sur de la marche sur sol plat améliorant les performances et ajoutant des fonctionnalitées au précédent algorithme. En collaborant avec des spécialistes du mouvement humain nous avons implementé un contrôleur innovant permettant de suivre des trajectoires cycliques du centre de masse. Nous présenterons aussi un contrôleur corps-complet utilisant, pour le haut du corps, des primitives de mouvements extraites du mouvement humain et pour le bas du corps, un générateur de marche. Les résultats de cette thèse ont été intégrés dans la suite logicielle "Stack-of-Tasks" du LAAS-CNRS.This thesis covers the topic of humanoid robot locomotion in the frame of the European project KoroiBot. The goal of this project is to enhance the ability of humanoid robots to walk in a dynamic and versatile fashion as humans do. Research and innovation studies in KoroiBot rely on optimal control methods both for the identification of cost functions used by human being and for their implementations on robots owned by roboticist partners. Hence, this thesis includes fruitful collaborations with both control mathematicians and experts in motion primitive modeling. The main contributions of this PhD thesis lies in the design of new real time controllers for humanoid robot locomotion with our partners from the University of Heidelberg and their integration on the HRP-2 robot. Two controllers will be shown, one allowing multi-contact locomotion with a prior knowledge of the future contacts. And the second is an extension of a previous work improving performance and providing additional functionalities. In a collaboration with experts in human motion we designed an innovating controller for tracking cyclic trajectories of the center of mass. We also show a whole body controller using upper body movement primitives extracted from human behavior and lower body movement computed by a walking pattern generator. The results of this thesis have been integrated into the LAAS-CNRS "Stack-of-Tasks" software suit