Real-time biped character stepping

PhD ThesisA rudimentary biped activity that is essential in interactive evirtual worlds, such as video-games and training simulations, is stepping. For example, stepping is fundamental in everyday terrestrial activities that include walking and balance recovery. Therefore an effective 3D stepping control algorithm that is computationally fast and easy to implement is extremely valuable and important to character animation research. This thesis focuses on generating real-time controllable stepping motions on-the-fly without key-framed data that are responsive and robust (e.g.,can remain upright and balanced under a variety of conditions, such as pushes and dynami- cally changing terrain). In our approach, we control the character’s direction and speed by means of varying the stepposition and duration. Our lightweight stepping model is used to create coordinated full-body motions, which produce directable steps to guide the character with specific goals (e.g., following a particular path while placing feet at viable locations). We also create protective steps in response to random disturbances (e.g., pushes). Whereby, the system automatically calculates where and when to place the foot to remedy the disruption. In conclusion, the inverted pendulum has a number of limitations that we address and resolve to produce an improved lightweight technique that provides better control and stability using approximate feature enhancements, for instance, ankle-torque and elongated-body

Actuation-Aware Simplified Dynamic Models for Robotic Legged Locomotion

In recent years, we witnessed an ever increasing number of successful hardware implementations of motion planners for legged robots. If one common property is to be identified among these real-world applications, that is the ability of online planning. Online planning is forgiving, in the sense that it allows to relentlessly compensate for external disturbances of whatever form they might be, ranging from unmodeled dynamics to external pushes or unexpected obstacles and, at the same time, follow user commands. Initially replanning was restricted only to heuristic-based planners that exploit the low computational effort of simplified dynamic models. Such models deliberately only capture the main dynamics of the system, thus leaving to the controllers the issue of anchoring the desired trajectory to the whole body model of the robot. In recent years, however, we have seen a number of new approaches attempting to increase the accuracy of the dynamic formulation without trading-off the computational efficiency of simplified models. In this dissertation, as an example of successful hardware implementation of heuristics and simplified model-based locomotion, I describe the framework that I developed for the generation of an omni-directional bounding gait for the HyQ quadruped robot. By analyzing the stable limit cycles for the sagittal dynamics and the Center of Pressure (CoP) for the lateral stabilization, the described locomotion framework is able to achieve a stable bounding while adapting to terrains of mild roughness and to sudden changes of the user desired linear and angular velocities. The next topic reported and second contribution of this dissertation is my effort to formulate more descriptive simplified dynamic models, without trading off their computational efficiency, in order to extend the navigation capabilities of legged robots to complex geometry environments. With this in mind, I investigated the possibility of incorporating feasibility constraints in these template models and, in particular, I focused on the joint torques limits which are usually neglected at the planning stage. In this direction, the third contribution discussed in this thesis is the formulation of the so called actuation wrench polytope (AWP), defined as the set of feasible wrenches that an articulated robot can perform given its actuation limits. Interesected with the contact wrench cone (CWC), this yields a new 6D polytope that we name feasible wrench polytope (FWP), defined as the set of all wrenches that a legged robot can realize given its actuation capabilities and the friction constraints. Results are reported where, thanks to efficient computational geometry algorithms and to appropriate approximations, the FWP is employed for a one-step receding horizon optimization of center of mass trajectory and phase durations given a predefined step sequence on rough terrains. For the sake of reachable workspace augmentation, I then decided to trade off the generality of the FWP formulation for a suboptimal scenario in which a quasi-static motion is assumed. This led to the definition of the, so called, local/instantaneous actuation region and of the global actuation/feasible region. They both can be seen as different variants of 2D linear subspaces orthogonal to gravity where the robot is guaranteed to place its own center of mass while being able to carry its own body weight given its actuation capabilities. These areas can be intersected with the well known frictional support region, resulting in a 2D linear feasible region, thus providing an intuitive tool that enables the concurrent online optimization of actuation consistent CoM trajectories and target foothold locations on rough terrains

Fondements calculatoires de la locomotion anthropomorphe

La locomotion anthropomorphe est un processus complexe qui met en jeu un très grand nombre de degrés de liberté, le corps humain disposant de plus de trois cents articulations contre une trentaine chez les robots humanoïdes. Pris dans leur ensemble, ces degrés de liberté montrent une certaine cohérence rendant possible la mise en mouvement du système anthropomorphe et le maintien de son équilibre, dans le but d'éviter la chute. Cette thèse met en lumière les fondements calculatoires à l'origine de cette orchestration. Elle introduit un cadre mathématique unifié permettant à la fois l'étude de la locomotion humaine, et la génération de trajectoires locomotrices pour les robots humanoïdes. Ce cadre consiste en une réduction de la dynamique corps-complet du système pour ne considérer que sa projection autour du centre de gravité, aussi appelée dynamique centroïdale. Bien que réduite, nous montrons que cette dynamique centroïdale joue un rôle central dans la compréhension et la formation des mouvements locomoteurs. Pour ce faire, nous établissons dans un premier temps les conditions d'observabilité de cette dynamique, c'est-à-dire que nous montrons dans quelle mesure cette donnée peut être appréhendée à partir des capteurs couramment employés en biomécanique et en robotique. Forts de ces conditions d'observabilité, nous proposons un estimateur capable de reconstruire la position non-biaisée du centre de gravité. A partir de cet estimateur et de l'acquisition de mouvements de marche sur divers sujets, nous mettons en évidence la présence d'un motif cycloïdal du centre de gravité dans le plan sagittal lorsque l'humain marche de manière nominale, c'est-à-dire sans y penser. La présence de ce motif suggère l'existence d'une synergie motrice jusqu'alors ignorée, soutenant la théorie d'une coordination générale des mouvements pendant la locomotion. La dernière contribution de cette thèse porte sur la locomotion multi-contacts. Les humains ont une agilité remarquable pour effectuer des mouvements locomoteurs qui nécessitent l'utilisation conjointe des bras et des jambes, comme lors de l'ascension d'une paroi rocheuse. Comment doter les robots humanoïdes de telles capacités ? La difficulté n'est certainement pas technologique, puisque les robots actuels sont capables de développer des puissances mécaniques suffisantes. Leurs performances, évaluées tant en termes de qualité des mouvements que de temps de calcul, restent très limitées. Dans cette thèse, nous abordons le problème de génération de trajectoires multi-contacts sous la forme d'un problème de commande optimale. L'intérêt de cette formulation est de partir du modèle réduit de la dynamique centroïdale tout en répondant aux contraintes d'équilibre. L'idée originale consiste à maximiser la vraisemblance de cette dynamique réduite vis-à-vis de la dynamique corps-complet. Elle repose sur l'apprentissage d'une mesure d'occupation qui reflète les capacités cinématiques et dynamiques du robot. Elle est effective : l'algorithmique qui en découle est compatible avec des applications temps réel. L'approche a été évaluée avec succès sur le robot humanoïde HRP-2, sur plusieurs modes de locomotions, démontrant ainsi sa polyvalence.Anthropomorphic locomotion is a complex process that involves a very large number of degrees of freedom, the human body having more than three hundred joints against thirty in humanoid robots. Taken as a whole, these degrees of freedom show a certain coherence making it possible to set the anthropomorphic system in motion and maintain its equilibrium, in order to avoid falling. This thesis highlights the computational foundations behind this orchestration. It introduces a unified mathematical framework allowing both the study of human locomotion and the generation of locomotive trajectories for humanoid robots. This framework consists of a reduction of the body-complete dynamics of the system to consider only its projection around the center of gravity, also called centroid dynamics. Although reduced, we show that this centroidal dynamics plays a central role in the understanding and formation of locomotive movements. To do this, we first establish the observability conditions of this dynamic, that is to say that we show to what extent this data can be apprehended from sensors commonly used in biomechanics and robotics. Based on these observability conditions, we propose an estimator able to reconstruct the unbiased position of the center of gravity. From this estimator and the acquisition of walking motions on various subjects, we highlight the presence of a cycloidal pattern of the center of gravity in the sagittal plane when the human is walking nominally, that is, to say without thinking. The presence of this motif suggests the existence of a motor synergy hitherto unknown, supporting the theory of a general coordination of movements during locomotion. The last contribution of this thesis is on multi-contact locomotion. Humans have remarkable agility to perform locomotive movements that require joint use of the arms and legs, such as when climbing a rock wall. How to equip humanoid robots with such capabilities? The difficulty is certainly not technological, since current robots are able to develop sufficient mechanical powers. Their performances, evaluated both in terms of quality of movement and computing time, remain very limited. In this thesis, we address the problem of generating multi-contact trajectories in the form of an optimal control problem. The interest of this formulation is to start from the reduced model of centroid dynamics while responding to equilibrium constraints. The original idea is to maximize the likelihood of this reduced dynamic with respect to body-complete dynamics. It is based on learning a measurement of occupation that reflects the kinematic and dynamic capabilities of the robot. It is effective: the resulting algorithmic is compatible with real-time applications. The approach has been successfully evaluated on the humanoid robot HRP-2, on several modes of locomotion, thus demonstrating its versatility

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

Climbing and Walking Robots

Nowadays robotics is one of the most dynamic fields of scientific researches. The shift of robotics researches from manufacturing to services applications is clear. During the last decades interest in studying climbing and walking robots has been increased. This increasing interest has been in many areas that most important ones of them are: mechanics, electronics, medical engineering, cybernetics, controls, and computers. Today’s climbing and walking robots are a combination of manipulative, perceptive, communicative, and cognitive abilities and they are capable of performing many tasks in industrial and non- industrial environments. Surveillance, planetary exploration, emergence rescue operations, reconnaissance, petrochemical applications, construction, entertainment, personal services, intervention in severe environments, transportation, medical and etc are some applications from a very diverse application fields of climbing and walking robots. By great progress in this area of robotics it is anticipated that next generation climbing and walking robots will enhance lives and will change the way the human works, thinks and makes decisions. This book presents the state of the art achievments, recent developments, applications and future challenges of climbing and walking robots. These are presented in 24 chapters by authors throughtot the world The book serves as a reference especially for the researchers who are interested in mobile robots. It also is useful for industrial engineers and graduate students in advanced study

Receding-horizon motion planning of quadrupedal robot locomotion

Quadrupedal robots are designed to offer efficient and robust mobility on uneven terrain. This thesis investigates combining numerical optimization and machine learning methods to achieve interpretable kinodynamic planning of natural and agile locomotion. The proposed algorithm, called Receding-Horizon Experience-Controlled Adaptive Legged Locomotion (RHECALL), uses nonlinear programming (NLP) with learned initialization to produce long-horizon, high-fidelity, terrain-aware, whole-body trajectories. RHECALL has been implemented and validated on the ANYbotics ANYmal B and C quadrupeds on complex terrain. The proposed optimal control problem formulation uses the single-rigid-body dynamics (SRBD) model and adopts a direct collocation transcription method which enables the discovery of aperiodic contact sequences. To generate reliable trajectories, we propose fast-to-compute analytical costs that leverage the discretization and terrain-dependent kinematic constraints. To extend the formulation to receding-horizon planning, we propose a segmentation approach with asynchronous centre of mass (COM) and end-effector timings and a heuristic initialization scheme which reuses the previous solution. We integrate real-time 2.5D perception data for online foothold selection. Additionally, we demonstrate that a learned stability criterion can be incorporated into the planning framework. To accelerate the convergence of the NLP solver to locally optimal solutions, we propose data-driven initialization schemes trained using supervised and unsupervised behaviour cloning. We demonstrate the computational advantage of the schemes and the ability to leverage latent space to reconstruct dynamic segments of plans which are several seconds long. Finally, in order to apply RHECALL to quadrupeds with significant leg inertias, we derive the more accurate lump leg single-rigid-body dynamics (LL-SRBD) and centroidal dynamics (CD) models and their first-order partial derivatives. To facilitate intuitive usage of costs, constraints and initializations, we parameterize these models by Euclidean-space variables. We show the models have the ability to shape rotational inertia of the robot which offers potential to further improve agility

Towards Robust Bipedal Locomotion:From Simple Models To Full-Body Compliance

Thanks to better actuator technologies and control algorithms, humanoid robots to date can perform a wide range of locomotion activities outside lab environments. These robots face various control challenges like high dimensionality, contact switches during locomotion and a floating-base nature which makes them fall all the time. A rich set of sensory inputs and a high-bandwidth actuation are often needed to ensure fast and effective reactions to unforeseen conditions, e.g., terrain variations, external pushes, slippages, unknown payloads, etc. State of the art technologies today seem to provide such valuable hardware components. However, regarding software, there is plenty of room for improvement. Locomotion planning and control problems are often treated separately in conventional humanoid control algorithms. The control challenges mentioned above are probably the main reason for such separation. Here, planning refers to the process of finding consistent open-loop trajectories, which may take arbitrarily long computations off-line. Control, on the other hand, should be done very fast online to ensure stability. In this thesis, we want to link planning and control problems again and enable for online trajectory modification in a meaningful way. First, we propose a new way of describing robot geometries like molecules which breaks the complexity of conventional models. We use this technique and derive a planning algorithm that is fast enough to be used online for multi-contact motion planning. Similarly, we derive 3LP, a simplified linear three-mass model for bipedal walking, which offers orders of magnitude faster computations than full mechanical models. Next, we focus more on walking and use the 3LP model to formulate online control algorithms based on the foot-stepping strategy. The method is based on model predictive control, however, we also propose a faster controller with time-projection that demonstrates a close performance without numerical optimizations. We also deploy an efficient implementation of inverse dynamics together with advanced sensor fusion and actuator control algorithms to ensure a precise and compliant tracking of the simplified 3LP trajectories. Extensive simulations and hardware experiments on COMAN robot demonstrate effectiveness and strengths of our method. This thesis goes beyond humanoid walking applications. We further use the developed modeling tools to analyze and understand principles of human locomotion. Our 3LP model can describe the exchange of energy between human limbs in walking to some extent. We use this property to propose a metabolic-cost model of human walking which successfully describes trends in various conditions. The intrinsic power of the 3LP model to generate walking gaits in all these conditions makes it a handy solution for walking control and gait analysis, despite being yet a simplified model. To fill the reality gap, finally, we propose a kinematic conversion method that takes 3LP trajectories as input and generates more human-like postures. Using this method, the 3LP model, and the time-projecting controller, we introduce a graphical user interface in the end to simulate periodic and transient human-like walking conditions. We hope to use this combination in future to produce faster and more human-like walking gaits, possibly with more capable humanoid robots

Kinematic and dynamic analysis for biped robots design

En esta tesis un nuevo método para encontrar sistemas dinámicamente equivalentes es propuesto. El objetivo es el de crear una herramienta para el análisis de robots bípedos. La herramienta consiste en modelos simplificados obtenidos del principio de equivalencia dinámica, que dice que si dos sistemas poseen la misma masa, el mismo centro de masa y el mismo momento de inercia, entonces son dinámicamente equivalentes. Este concepto no es nuevo y es comúnmente utilizado en el diseño de máquinas alternativas, o para encontrar el sweet spot de objetos esbeltos tales como bates o espadas. Con la aplicación del principio de equivalencia dinámica se encuentra el centro de percusión. La aportación en esta tesis es la aplicación de este concepto al análisis de robots bípedos, y la extensión del centro de percusión a cadenas cinemáticas. La herramienta fundamental para la obtención de resultados de investigación en esta tesis hace uso del lenguaje de simulación Modelica®. Las simulaciones son altamente detalladas gracias a la librería estándar Multibody incluida en las especificaciones del mismo. Como consecuencia de los trabajos desarrollados se crearon nuevas clases para extender la capacidad de la librería y aplicarla a m´aquinas caminantes. El desarrollo de esta tesis está centrado en el desarrollo de dos modelos. El primero es un péndulo invertido equivalente, con la característica que posee las mismas propiedades dinámicas del robot que modela. Dichas propiedades son la masas total, el centro de masa y el momento de inercia. Este modelo es luego utilizado para generar el caminar de un bípedo simple. El bípedo es simulado con un volante de inercia como cuerpo, y pies de contacto puntual. Posee rodillas y está totalmente actuado. Los eslabones del robot poseen propiedades de sólido rígido y ninguna simplificación ha sido considerada. El segundo modelo tiene el objetivo de imitar la topología del bípedo que representa, por lo tanto tiene un grado mayor de complejidad que el anterior. Este modelo es construido al dividir al robot en tres grupos: Las dos piernas, y otro grupo compuesto por la cabeza, los brazos y el torso (Denominado HAT por sus siglas en inglés). Este modelo es denominado modelo de cuatro masas puntuales. Este modelo es posteriormente validado utilizándolo para desacoplar la dinámica del sistema, la única información utilizada para llevar a cabo esta tarea es proporcionada por dicho modelo. ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------In this thesis a method to find dynamically equivalent systems is proposed. The objective is to provide a tool to analyze biped robots by simplifying their dynamics to simpler models. The equivalent models are obtained with the concept of dynamic equivalence that states that if two systems share the same total mass, the same center of mass, and the same moment of inertia then they are considered to be dynamically equivalent. This concept is not new and it is used in the design of alternative machines, or to find the sweet spot of long object like swords or bats. The result of the application of the dynamic equivalence principle is the point known as the center of percussion. The novelty in this thesis is to apply this concept to the analysis of biped robots, and the extension of the center of percussion to kinematic chains. The work in this thesis developed with the help of the simulation language Modelica®. The simulations are very detailed by implementing elaborated rigid body dynamics provided by the multibody standard library included in the language specifications. New classes were created in order to be able to simulate walking machines. Those classes introduce contact objects at ground foot interactions and mechanical stops for knee joints. The development of this thesis is centered around the proposal of two models. The first model is an equivalent inverted pendulum with the characteristic that it has the same dynamic properties, i.e., total mass, center of mass and moment of inertia, of the biped that models. This model is later used to synthesize gait in a simple, but realistic biped. The biped is simulated with a flywheel body, and point feet. It has knees and it is fully actuated. Also all the links have complete rigid body properties and no simplifications were done. The second model has the objective to resemble the topology of the biped it represents, therefore it is slightly more complex than the equivalent inverted pendulum. This model is constructed by grouping the components of the robot in three groups: Two legs and the HAT group (HAT stands for head, arms and trunk). This model is denominated four point masses model. The model is later validated by decoupling the dynamics of the system only with the information provided by the four point masses model

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