Safe 3D Bipedal Walking through Linear MPC with 3D Capturability

International audienceWe propose a linear MPC scheme for online computation of reactive walking motions, necessary for fast interactions such as physical collaboration with humans or collision avoidance in crowds. Unlike other existing schemes, it provides fully adaptable height, adaptable step placement and complete kinematic and dynamic feasibility guarantees, making it possible to walk perfectly safely on a piecewise horizontal ground such as stairs. A linear formulation is proposed, based on efficiently bounding the nonlinear term introduced by vertical motion, considering two linear constraints instead of one nonlinear constraint. Balance and Passive Safety guarantees are secured by enforcing a 3D capturability constraint. Based on a comparison between CoM and CoP trajectories involving exponentials instead of polynomials, this capturability constraint involves a CoM motion stopping along a segment of line, always maintaining complete kinematic and dynamic feasibility

Motion planning and control methods for nonprehensile manipulation and multi-contact locomotion tasks

Many existing works in the robotic literature deal with the problem of nonprehensile dynamic manipulation. However, a unified control framework does not exist so far. One of the ambitious goals of this Thesis is to contribute to identify planning and control frameworks solving classes of nonprehensile dynamic manipulation tasks, dealing with the non linearity of their dynamic models and, consequently, with the inherited design complexity. Besides, while passing through a number of connections between dynamic nonprehensile manipulation and legged locomotion, the Thesis presents novel methods for generating walking motions in multi-contact situations

Model Predictive Control

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Motion Planning for Multi-Contact Visual Servoing on Humanoid Robots

International audienceThis paper describes the implementation of a canonical motion generation pipeline guided by vision for a TALOS humanoid robot. The proposed system is using a mul-ticontact planner, a Differential Dynamic Programming (DDP) algorithm, and a stabilizer. The multicontact planner provides a set of contacts and dynamically consistent trajectories for the Center-Of-Mass (CoM) and the Center-Of-Pressure (CoP). It provides a structure to initialize a DDP algorithm which, in turn, provides a dynamically consistent trajectory for all the joints as it integrates all the dynamics of the robot, together with rigid contact models and the visual task. Tested on Gazebo the resulting trajectory had to be stabilized with a state-of-the-art algorithm to be successful. In addition to testing motion generated from high specifications to the stabilized motion in simulation, we express visual features at Whole Body Generator level which is a DDP formulated solver. It handles non-linearities as the ones introduced by the projections of visual features expressed and minimized in the image plan of the camera

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

Predictive Whole-Body Control of Humanoid Robot Locomotion

Humanoid robots are machines built with an anthropomorphic shape. Despite decades of research into the subject, it is still challenging to tackle the robot locomotion problem from an algorithmic point of view. For example, these machines cannot achieve a constant forward body movement without exploiting contacts with the environment. The reactive forces resulting from the contacts are subject to strong limitations, complicating the design of control laws. As a consequence, the generation of humanoid motions requires to exploit fully the mathematical model of the robot in contact with the environment or to resort to approximations of it. This thesis investigates predictive and optimal control techniques for tackling humanoid robot motion tasks. They generate control input values from the system model and objectives, often transposed as cost function to minimize. In particular, this thesis tackles several aspects of the humanoid robot locomotion problem in a crescendo of complexity. First, we consider the single step push recovery problem. Namely, we aim at maintaining the upright posture with a single step after a strong external disturbance. Second, we generate and stabilize walking motions. In addition, we adopt predictive techniques to perform more dynamic motions, like large step-ups. The above-mentioned applications make use of different simplifications or assumptions to facilitate the tractability of the corresponding motion tasks. Moreover, they consider first the foot placements and only afterward how to maintain balance. We attempt to remove all these simplifications. We model the robot in contact with the environment explicitly, comparing different methods. In addition, we are able to obtain whole-body walking trajectories automatically by only specifying the desired motion velocity and a moving reference on the ground. We exploit the contacts with the walking surface to achieve these objectives while maintaining the robot balanced. Experiments are performed on real and simulated humanoid robots, like the Atlas and the iCub humanoid robots

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

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