Motion Planning and Control of Dynamic Humanoid Locomotion

Inspired by human, humanoid robots has the potential to become a general-purpose platform that lives along with human. Due to the technological advances in many field, such as actuation, sensing, control and intelligence, it finally enables humanoid robots to possess human comparable capabilities. However, humanoid locomotion is still a challenging research field. The large number of degree of freedom structure makes the system difficult to coordinate online. The presence of various contact constraints and the hybrid nature of locomotion tasks make the planning a harder problem to solve. Template model anchoring approach has been adopted to bridge the gap between simple model behavior and the whole-body motion of humanoid robot. Control policies are first developed for simple template models like Linear Inverted Pendulum Model (LIPM) or Spring Loaded Inverted Pendulum(SLIP), the result controlled behaviors are then been mapped to the whole-body motion of humanoid robot through optimization-based task-space control strategies. Whole-body humanoid control framework has been verified on various contact situations such as unknown uneven terrain, multi-contact scenarios and moving platform and shows its generality and versatility. For walking motion, existing Model Predictive Control approach based on LIPM has been extended to enable the robot to walk without any reference foot placement anchoring. It is kind of discrete version of \u201cwalking without thinking\u201d. As a result, the robot could achieve versatile locomotion modes such as automatic foot placement with single reference velocity command, reactive stepping under large external disturbances, guided walking with small constant external pushing forces, robust walking on unknown uneven terrain, reactive stepping in place when blocked by external barrier. As an extension of this proposed framework, also to increase the push recovery capability of the humanoid robot, two new configurations have been proposed to enable the robot to perform cross-step motions. For more dynamic hopping and running motion, SLIP model has been chosen as the template model. Different from traditional model-based analytical approach, a data-driven approach has been proposed to encode the dynamics of the this model. A deep neural network is trained offline with a large amount of simulation data based on the SLIP model to learn its dynamics. The trained network is applied online to generate reference foot placements for the humanoid robot. Simulations have been performed to evaluate the effectiveness of the proposed approach in generating bio-inspired and robust running motions. The method proposed based on 2D SLIP model can be generalized to 3D SLIP model and the extension has been briefly mentioned at the end

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

Dynamic Balance and Gait Metrics for Robotic Bipeds

For legged robots to be useful in the real world, they must be able to balance and walk reliably. Both of these abilities improve when a system is more effective at moving itself around relative to its contacts (i.e., its feet). Achieving this type of movement depends both on the controller used to perform the motion and the physical properties of the system. Although much work has been done on the development of dynamic controllers for balance and gait, only limited research exists on how to quantify a system’s physical balance capabilities or how to modify the system to improve those capabilities. From the control perspective, there are three strategies for maintaining balance in bipeds: flexing, leaning, and stepping. Both stepping and leaning strategies typically depend on balance points (critical points used for maintaining or regaining balance) to determine whether or not a step is needed, and if so, where to step. Although several balance point estimators exist, the majority of these methods make undesirable assumptions (e.g., ignoring the impact dynamics, assuming massless legs, planar motion, etc.). From the physical design perspective, one promising approach for analyzing system performance is a set of dynamic ratios called velocity and momentum gains, which are dependent only on the (scale-invariant) dynamic parameters and instantaneous configuration of a system, enabling entire classes of mechanisms to be analyzed at the same time. This thesis makes four key contributions towards improving biped balancing capabilities. First, a dynamic bipedal controller is proposed which uses a 3D balance point estimator both to respond to disturbances and produce reliable stepping. Second, a novel balance point estimator is proposed that facilitates stepping while combining and expanding the features of existing 2D and 3D estimators to produce a generalized 3D formulation. Third, the momentum gain formulation is extended to general 2D and 3D systems, then both gains are compared to centroidal momentum via a spatial formulation and incorporated into a generalized gain definition. Finally, the gains are used as a metric in an optimization framework to design parameterized balancing mechanisms within a given configuration space. Effectively, this enables an optimization of how well a system could balance without the need to pre-specify or co-generate controllers and/or trajectories. To validate the control contributions, simulated bipeds are subjected to external disturbances while standing still and walking. For the gain contributions, the framework is used to compare gain-optimized mechanisms to those based on the cost of transport metric. Through the combination of gain-based physical design optimization and the use of predictive, real-time balance point estimators within dynamic controllers, bipeds and other legged systems will soon be able to achieve reliable balance and gait in the real world

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

Mechanics and Control of Human Balance

A predictive, forward-dynamic model and computer simulation of human gait has important medical and research applications. Most human simulation work has focused on inverse dynamics studies to quantify bone on bone forces and muscle loads. Inverse dynamics is not predictive - it works backwards from experimentally measured motions in an effort to find the forces that caused the motion. In contrast, forward dynamics determines how a mechanism will move without the need for experimentation. Most of the forward dynamic gait simulations reported consider only one step, foot contact is not modeled, and balance controllers are not used. This thesis addresses a few of the shortcomings of current human gait simulations by contributing an experimentally validated foot contact model, a model-based stance controller, and an experimentally validated model of the relationship between foot placement location and balance. The goal of a predictive human gait simulation is to determine how a human would walk under a condition of interest, such as walking across a slippery floor, using a new lower limb prosthesis, or with reduced leg strength. To achieve this goal, often many different gaits are simulated and the one that is the most human-like is chosen as the prediction for how a person would move. Thus it is necessary to quantify how `human-like' a candidate gait is. Human walking is very efficient, and so, the metabolic efficiency of the candidate gait is most often used to measure the performance of a candidate gait. Muscles consume metabolic energy as a function of the tension they develop and the rate at which they are contracting. Muscle tension is developed, and contractions are made in an effort generate torques about joints in order to make them move. To predict human gait, it is necessary for the simulation to be able to walk in such a way that the simulated leg joints use similar joint torques and kinematics as a human leg does, all while balancing the body. The joint torques that the legs must develop to propel the body forward, and balance it, are heavily influenced by the ground reaction forces developed between the simulated foot and the ground. A predictive gait simulation must be able to control the model so that it can walk, and remain balanced while generating ground reaction force profiles that are similar to experimentally observed human ground reaction force profiles. Ground reaction forces are shaped by the way the foot interacts with the ground, making it very important to model the human foot accurately. Most continuous foot contact models present in the literature have been experimentally validated using pendulum impact methods that have since been shown to produce inaccurate results. The planar foot contact model developed as part of this research was validated in-vivo using conventional force plates and optical tracking markers. The experimental data was also highly useful for developing a computationally efficient foot model by identifying the dominant contact properties of a real foot (during walking), without the complexity of modelling the 26 bones, 33 joints, over 90 ligaments, and the network of muscles that are in a real foot. Both ground reaction forces and the balance of the model are heavily influenced by the way the stance limb is controlled. Anthropomorphic multibody models typically have a fragile sense of balance, and ground reaction force profiles that do not look similar to experimentally measured human ground reaction force profiles. In contrast, the simple point-mass spring-loaded-inverted-pendulum (SLIP) can be made to walk or run in a balanced manner with center-of-mass (COM) kinematics and ground reaction force profiles that could be mistaken for the equivalent human data. A stance limb controller is proposed that uses a planar SLIP to compute a reference trajectory for a planar anthropomorphic multibody gait model. The torso of the anthropomorphic model is made to track the computed trajectory of the SLIP using a control system. The aim of this partitioned approach to gait simulation is to endow the anthropomorphic model with the human-like gait of the simpler SLIP model. Although the SLIP model-based stance-controller allows an anthropomorphic gait model to walk in more human-like manner, it also inherits the short comings of the SLIP model. The SLIP can walk or run like a human, but only at a fixed velocity. It cannot initiate or terminate gait. Fall preventing movements, such as gait termination and compensatory stepping, are of particular relevance to kinesiologists and health care professionals. Kinesiologists have known for nearly a decade that humans restore their balance primarily by systematically altering their foot placement location. This thesis presents a human experimental validation of a planar foot placement algorithm that was originally designed to restore the balance of bipedal robots. A three-dimensional (3D) theoretical extension to the planar foot placement algorithm is also presented along with preliminary human experimental results. These models of foot placement can be used in the future to improve the capabilities of gait simulations by giving simple models human-like compensatory stepping abilities. The theoretical extension also provides some insight into how instability and balance performance can be quantified. The instability and balance performance measures have important applications for diagnosing and rehabilitating balance problems. Despite all of the progress that has been made, there is still much work to be done. Work needs to be continued to find methods that allow the anthropomorphic model to emulate the SLIP model more faithfully. Experimental work needs to be completed to realize the potential diagnostic and rehabilitation applications of the foot placement models. With continued effort, a predictive, balanced, multi-step gait simulation can be developed that will give researchers the time-saving capability of computerized hypothesis testing, and medical professionals improved diagnostic and rehabilitation methods

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

A Loosely-Coupled Passive Dynamics and Finite Element based Model for Minimising Biomechanically Driven Unhealthy Joint Loads during Walking in Transtibial Amputees

The primary objective of a prosthetic foot is to improve the quality of life for amputees by enabling them to walk in a similar way to healthy individuals. Amputees su˙er from health risks including joint pain, back pain and joint inflammation. The aim of this thesis is to develop a new computational approach to reduce the likelihood of biomechanically driven joint pain in transtibial amputees resulting from sustained exposure to Unhealthy Loads (ULs) during walking. This is achieved by developing a computational methodology to achieve a customisable sti˙ness design solution for prosthetic feet so that the occurrence of unhealthy joint loads during walking is minimised.It is assumed that the healthy population is able to spend energy most optimally during walking at all walking speeds. During walking, the force exerted by the body on the ground is measured by the ground reaction force (GRF). The GRF value is normalised with the body weight defining a dimensionless parameter . The values are similar for both legs in healthy populations but are di˙erent for the sound and a˙ected leg for amputees. A new hypothesis has been proposed in this thesis that walking is comfortable for an amputee when the di˙erence between values is minimal between the amputee and an equivalent healthy population. The values for healthy adults, as well as amputees, follow a finite number of patterns. The pattern of the values (or the GRF curve) depends on the walking speed of an individual, categorised as slow, fast or free walking. However, it is observed in the literature that free walking speed (FWS) varies over a wide range for healthy individuals (e.g. 1.1 m/s to 1.5 m/s). As a result, it was diÿcult to establish a relationship between walking speed and GRF pattern. A novel parametrised description of GRF curves for a healthy population and amputees is proposed so that a new dimensionless velocity ratio parameter and the corresponding value of the FWS can be predicted by observing the GRF pattern of a healthy adult or an amputee. A new classification approach based on the parametrised description of GRF curves, along with the dimensionless velocity ratio parameter, has been recommended for categorising very slow, slow, free, fast and very fast walking. The GRF result predictions are validated on healthy adults in an experiment conducted in a gait lab. A group of candidates who walk a lot in their daily life were specially selected for this experiment. This classification approach is used to develop a new measure of ULs based on the parametrised GRF description for healthy population and amputees. An innovative computational methodology is proposed to design an optimal sti˙ness response of a prosthetic foot that minimises the occurrence of ULs. This is achieved by transferring the roll-over shape (ROS) information of the prosthetic foot and the corresponding information for a given velocity ratio across a passive walking dynamic (PWD) and a finite element model via a newly defined form of loose coupling. A theoretical case study is presented in which an amputee walks in a gait lab with a representative C-shaped prosthetic foot. The thesis explains how the proposed novel computational methodology is able to redesign the prosthetic foot in a way that is better suited to minimising ULs. The redesign process of the prosthetic foot has led to the development of an innovative 3D printable double keel and double heel design. With the advancement of carbon reinforced polymers and additive manufacturing technology, the sti˙ness customisation methodology proposed in this thesis has the potential to create a new generation of energy-eÿcient prosthetic feet