Dynamic whole-body motion generation under rigid contacts and other unilateral constraints

The most widely used technique for generating wholebody motions on a humanoid robot accounting for various tasks and constraints is inverse kinematics. Based on the task-function approach, this class of methods enables the coordination of robot movements to execute several tasks in parallel and account for the sensor feedback in real time, thanks to the low computation cost. To some extent, it also enables us to deal with some of the robot constraints (e.g., joint limits or visibility) and manage the quasi-static balance of the robot. In order to fully use the whole range of possible motions, this paper proposes extending the task-function approach to handle the full dynamics of the robot multibody along with any constraint written as equality or inequality of the state and control variables. The definition of multiple objectives is made possible by ordering them inside a strict hierarchy. Several models of contact with the environment can be implemented in the framework. We propose a reduced formulation of the multiple rigid planar contact that keeps a low computation cost. The efficiency of this approach is illustrated by presenting several multicontact dynamic motions in simulation and on the real HRP-2 robot

Multi-contact Walking Pattern Generation based on Model Preview Control of 3D COM Accelerations

We present a multi-contact walking pattern generator based on preview-control of the 3D acceleration of the center of mass (COM). A key point in the design of our algorithm is the calculation of contact-stability constraints. Thanks to a mathematical observation on the algebraic nature of the frictional wrench cone, we show that the 3D volume of feasible COM accelerations is a always a downward-pointing cone. We reduce its computation to a convex hull of (dual) 2D points, for which optimal O(n log n) algorithms are readily available. This reformulation brings a significant speedup compared to previous methods, which allows us to compute time-varying contact-stability criteria fast enough for the control loop. Next, we propose a conservative trajectory-wide contact-stability criterion, which can be derived from COM-acceleration volumes at marginal cost and directly applied in a model-predictive controller. We finally implement this pipeline and exemplify it with the HRP-4 humanoid model in multi-contact dynamically walking scenarios

Offline and Online Planning and Control Strategies for the Multi-Contact and Biped Locomotion of Humanoid Robots

In the past decades, the Research on humanoid robots made progress forward accomplishing exceptionally dynamic and agile motions. Starting from the DARPA Robotic Challenge in 2015, humanoid platforms have been successfully employed to perform more and more challenging tasks with the eventual aim of assisting or replacing humans in hazardous and stressful working situations. However, the deployment of these complex machines in realistic domestic and working environments still represents a high-level challenge for robotics. Such environments are characterized by unstructured and cluttered settings with continuously varying conditions due to the dynamic presence of humans and other mobile entities, which cannot only compromise the operation of the robotic system but can also pose severe risks both to the people and the robot itself due to unexpected interactions and impacts. The ability to react to these unexpected interactions is therefore a paramount requirement for enabling the robot to adapt its behavior to the task needs and the characteristics of the environment. Further, the capability to move in a complex and varying environment is an essential skill for a humanoid robot for the execution of any task. Indeed, human instructions may often require the robot to move and reach a desired location, e.g., for bringing an object or for inspecting a specific place of an infrastructure. In this context, a flexible and autonomous walking behavior is an essential skill, study of which represents one of the main topics of this Thesis, considering disturbances and unfeasibilities coming both from the environment and dynamic obstacles that populate realistic scenarios.  Locomotion planning strategies are still an open theme in the humanoids and legged robots research and can be classified in sample-based and optimization-based planning algorithms. The first, explore the configuration space, finding a feasible path between the start and goal robot’s configuration with different logic depending on the algorithm. They suffer of a high computational cost that often makes difficult, if not impossible, their online implementations but, compared to their counterparts, they do not need any environment or robot simplification to find a solution and they are probabilistic complete, meaning that a feasible solution can be certainly found if at least one exists. The goal of this thesis is to merge the two algorithms in a coupled offline-online planning framework to generate an offline global trajectory with a sample-based approach to cope with any kind of cluttered and complex environment, and online locally refine it during the execution, using a faster optimization-based algorithm that more suits an online implementation. The offline planner performances are improved by planning in the robot contact space instead of the whole-body robot configuration space, requiring an algorithm that maps the two state spaces.   The framework proposes a methodology to generate whole-body trajectories for the motion of humanoid and legged robots in realistic and dynamically changing environments.  This thesis focuses on the design and test of each component of this planning framework, whose validation is carried out on the real robotic platforms CENTAURO and COMAN+ in various loco-manipulation tasks scenarios. &nbsp

Stable locomotion of humanoid robots based on mass concentrated model

El estudio de la locomoción de robots humanoides es actualmente un área muy activa, en el campo de la robótica. Partiendo del principio que el hombre esta construyendo robots para trabajar juntos cooperando en ambientes humanos. La estabilidad durante la caminata es un factor crítico que prevee la caída del robot, la cual puede causar deterioros al mismo y a las personas en su entorno. De esta manera, el presente trabajo pretende resolver una parte del problema de la locomoción bípeda, esto es los métodos empleados para “La generación del paso” (“Gait generation”) y asi obtener la caminata estable. Para obtener una marcha estable se utilizan modelos de masa concentrada. De esta manera el modelo del “pendulo invertido simple” y el modelo del “carro sobre la mesa” se han utilizado para conseguir la marcha estable de robots humanoides. En el modelo del pendulo invertido, la masa el pendulo conduce el movimiento del centro de gravedad (CDG) del robot humanoide durante la marcha. Se detallara que el CDG se mueve como una bola libre sobre un plano bajo las leyes del pendulo en el campo de gravedad. Mientras que en el modelo del “carro sobre la mesa”, el carro conduce el movimiento del CDG durante la marcha. En este caso, el movimiento del carro es tratado como un sistema servocontrolado, y el movimiento del CDG es obtenido con los actuales y futuros estados de referencia del Zero Moment Point (ZMP). El método para generar el paso propuesto esta compuesto de varias capas como son Movimiento global, movimiento local, generación de patrones de movimiento, cinemática inversa y dinámica inversa y finalmente una corrección off-line. Donde la entrada en este método es la meta global (es decir la configuración final del robot, en el entorno de marcha) y las salidas son los patrones de movimiento de las articulaciones junto con el patrón de referencia del ZMP. Por otro lado, se ha propuesto el método para generar el “Paso acíclico”. Este método abarca el movimiento del paso dinámico incluyendo todo el cuerpo del robot humanoide, desde desde cuaquier postura genérica estáticamente estable hasta otra; donde las entradas son los estados inicial y final del robot (esto es los ángulos iniciales y finales de las articulaciones) y las salidas son las trayectorias de referencia de cada articulación y del ZMP. Se han obtenido resultados satisfactorios en las simulaciones y en el robot humanoide real Rh-1 desarrollado en el Robotics lab de la Universidad Carlos III de Madrid. De igual manera el movimiento innovador llamado “Paso acíclico” se ha implemenado exitosamente en el robot humanoide HRP-2 (desarrollado por el AIST e Industrias Kawada Inc., Japon). Finalmente los resultados, contribuciones y trabajos futuros se expondran y discutirán. _______________________________________________The study of humanoid robot locomotion is currently a very active area in robotics, since humans build robots to work their environments in common cooperation and in harmony. Stability during walking motion is a critical fact in preventing the robot from falling down and causing the human or itself damages. This work tries to solve a part of the locomotion problem, which is, the “Gait Generation” methods used to obtain stable walking. Mass concentrated models are used to obtain stable walking motion. Thus the inverted pendulum model and the cart-table model are used to obtain stable walking motion in humanoid robots. In the inverted pendulum model, the mass of the pendulum drives the center of gravity (COG) motion of the humanoid robot while it is walking. It will be detailed that the COG moves like a free ball on a plane under the laws of the pendulum in the field of gravity. While in the cart-table model, the cart drives the COG motion during walking motion. In this case, the cart motion is treated as a servo control system, obtaining its motion from future reference states of the ZMP. The gait generation method proposed has many layers like Global motion, local motion, motion patterns generation, inverse kinematics and inverse dynamics and finally off-line correction. When the input in the gait generation method is the global goal (that is the final configuration of the robot in walking environment), and the output is the joint patterns and ZMP reference patterns. Otherwise, the “Acyclic gait” method is proposed. This method deals with the whole body humanoid robot dynamic step motion from any generic posture to another one when the input is the initial and goal robot states (that is the initial and goal joint angles) and the output is the joint and ZMP reference patterns. Successful simulation and actual results have been obtained with the Rh- 1 humanoid robot developed in the Robotics lab (Universidad Carlos III de Madrid, Spain) and the innovative motion called “Acyclic gait” implemented in the HRP-2 humanoid robot platform (developed by the AIST and Kawada Industries Inc., Japan). Furthermore, the results, contributions and future works will be discussed

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

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

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

Multi-contact planning and control for humanoid robots: Design and validation of a complete framework

In this paper, we consider the problem of generating appropriate motions for a torque- controlled humanoid robot that is assigned a multi-contact loco-manipulation task, i.e., a task that requires the robot to move within the environment by repeatedly establishing and breaking multiple, non-coplanar contacts. To this end, we present a complete multi-contact planning and control framework for multi-limbed robotic systems, such as humanoids. The planning layer works offline and consists of two sequential modules: first, a stance planner computes a sequence of feasible contact combinations; then, a whole-body planner finds the sequence of collision-free humanoid motions that realize them while respecting the physical limitations of the robot. For the challenging problem posed by the first stage, we propose a novel randomized approach that does not require the specification of pre-designed potential contacts or any kind of pre-computation. The control layer produces online torque commands that enable the humanoid to execute the planned motions while guaranteeing closed-loop balance. It relies on two modules, i.e., the stance switching and reactive balancing module; their combined action allows it to withstand possible execution inaccuracies, external disturbances, and modeling uncertainties. Numerical and experimental results obtained on COMAN+, a torque-controlled humanoid robot designed at Istituto Italiano di Tecnologia, validate our framework for loco-manipulation tasks of different complexity