Pattern Generation for Rough Terrain Locomotion with Quadrupedal Robots:Morphed Oscillators & Sensory Feedback

Animals are able to locomote on rough terrain without any apparent difficulty, but this does not mean that the locomotor system is simple. The locomotor system is actually a complex multi-input multi-output closed-loop control system. This thesis is dedicated to the design of controllers for rough terrain locomotion, for animal-like quadrupedal robots. We choose the problem of blind rough terrain locomotion as the target of experiments. Blind rough terrain locomotion requires continuous and momentary corrections of leg movements and body posture, and provides a proper testbed to observe the interaction of different mod- ules involved in locomotion control. As for the specific case of this thesis, we have to design rough terrain locomotion controllers that do not depend on the torque-control capability, have limited sensing, and have to be computationally light, all due to the properties of the robotics platform that we use. We propose that a robust locomotion controller, taking into account the aforementioned constraints, is constructed from at least three modules: 1) pattern generators providing the nominal patterns of locomotion; 2) A posture controller continuously adjusting the attitude of the body and keeping the robot upright; and 3) quick reflexes to react to unwanted momentary events like stumbling or an external force impulse. We introduce the framework of morphed oscillators to systematize the design of pattern gen- erators realized as coupled nonlinear oscillators. Morphed oscillators are nonlinear oscillators that can encode arbitrary limit cycle shapes and simultaneously have infinitely large basins of attraction. More importantly, they provide dynamical systems that can assume the role of feedforward locomotion controllers known as Central Pattern Generators (CPGs), and accept discontinuous sensory feedback without the risk of producing discontinuous output. On top of the CPG module, we add a kinematic model-based posture controller inspired by virtual model control (VMC), to control the body attitude. Virtual model control produces forces, and through the application of the Jacobian transpose method, generates torques which are added to the CPG torques. However, because our robots do not have a torque- control capability, we adapt the posture controller by producing task-space velocities instead of forces, thus generating joint-space velocity feedback signals. Since the CPG model used for locomotion generates joint velocities and accepts feedback without the fear of instability or discontinuity, the posture control feedback is easily integrated into the CPG dynamics. More- over, we introduce feedback signals for adjusting the posture by shifting the trunk positions, which directly update the limit cycle shape of the morphed oscillator nodes of the CPG. Reflexes are added, with minimal complexity, to react to momentary events. We implement simple impulse-based feedback mechanisms inspired by animals and successful rough terrain robots to 1) flex the leg if the robot is stumbling (stumbling correction reflex); 2) extend the leg if an expected contact is missing (leg extension reflex); or 3) initiate a lateral stepping sequence in response to a lateral external perturbation. CPG, posture controller, and reflexes are put together in a modular control architecture alongside additional modules that estimate inclination, control speed and direction, maintain timing of feedback signals, etc. [...

Chaotic exploration and learning of locomotor behaviours

Recent developments in the embodied approach to understanding the generation of adaptive behaviour, suggests that the design of adaptive neural circuits for rhythmic motor patterns should not be done in isolation from an appreciation, and indeed exploitation, of neural-body-environment interactions. Utilising spontaneous mutual entrainment between neural systems and physical bodies provides a useful passage to the regions of phase space which are naturally structured by the neuralbody- environmental interactions. A growing body of work has provided evidence that chaotic dynamics can be useful in allowing embodied systems to spontaneously explore potentially useful motor patterns. However, up until now there has been no general integrated neural system that allows goal-directed, online, realtime exploration and capture of motor patterns without recourse to external monitoring, evaluation or training methods. For the first time, we introduce such a system in the form of a fully dynamic neural system, exploiting intrinsic chaotic dynamics, for the exploration and learning of the possible locomotion patterns of an articulated robot of an arbitrary morphology in an unknown environment. The controller is modelled as a network of neural oscillators which are coupled only through physical embodiment, and goal directed exploration of coordinated motor patterns is achieved by a chaotic search using adaptive bifurcation. The phase space of the indirectly coupled neural-body-environment system contains multiple transient or permanent self-organised dynamics each of which is a candidate for a locomotion behaviour. The adaptive bifurcation enables the system orbit to wander through various phase-coordinated states using its intrinsic chaotic dynamics as a driving force and stabilises the system on to one of the states matching the given goal criteria. In order to improve the sustainability of useful transient patterns, sensory homeostasis has been introduced which results in an increased diversity of motor outputs, thus achieving multi-scale exploration. A rhythmic pattern discovered by this process is memorised and sustained by changing the wiring between initially disconnected oscillators using an adaptive synchronisation method. The dynamical nature of the weak coupling through physical embodiment allows this adaptive weight learning to be easily integrated, thus forming a continuous exploration-learning system. Our result shows that the novel neuro-robotic system is able to create and learn a number of emergent locomotion behaviours for a wide range of body configurations and physical environment, and can re-adapt after sustaining damage. The implications and analyses of these results for investigating the generality and limitations of the proposed system are discussed

Do humans drive spinal cord with limb velocity signal?

The ability to move in the environment is crucial to the survival of all animals. Neural pathways that control locomotion can be described as a hierarchy, with multiple levels of control, and those ultimately converge on spinal pattern generators. Neural pathways controlling locomotion are hierarchical, highly integrated, and well characterized anatomically, but functional explanations are lacking. Previous computational modeling of the CPG has proposed that they essential signal driving these spinal networks are expressed in the modality of desired velocity. To date, no published research has empirically tested velocity as being the control signal of locomotion. The purpose of this study was to evaluate human ability to discriminate inter-limb velocity on a split-belt treadmill. If the modality of locomotor control signal is indeed velocity then, according to the classical control theory, limb velocity should also be accurately sensed. We tested this hypothesis by probing human ability to detect minute changes in the velocity of each leg. Healthy volunteers with no previous history of neurological conditions or serious musculoskeletal damage to the lower extremities were recruited to walk on a split-belt treadmill with separately controlled belt speeds. Subjects were exposed to randomized asymmetric speeds of left and right legs for approximately 3 steps. A high-pitch cue instructed subjects to report the fastest leg. In addition, we tested velocity discrimination skills in two other conditions when subjects were either supported or loaded by 10% of their body weight. The perception threshold defined as the velocity detected with better than chance probability (above 50%) was 1.02+/-0.43% m/s, with no significant differences between body weight conditions. Variance of step cycle was found to significantly impact probability detection at the differential speed of 0.01 m/s, which is equivalent to the 1% detection level. The accurate velocity discrimination ability supports the idea that the velocity signal is represented within the locomotor control pathways. We propose that errors in this velocity signal are ultimately used to tune heading direction. Solving for the signal controlling locomotion has positive clinical implications, as it could be used in therapies such as locomotor rehabilitation following neurological injury

Humanoid Robots

For many years, the human being has been trying, in all ways, to recreate the complex mechanisms that form the human body. Such task is extremely complicated and the results are not totally satisfactory. However, with increasing technological advances based on theoretical and experimental researches, man gets, in a way, to copy or to imitate some systems of the human body. These researches not only intended to create humanoid robots, great part of them constituting autonomous systems, but also, in some way, to offer a higher knowledge of the systems that form the human body, objectifying possible applications in the technology of rehabilitation of human beings, gathering in a whole studies related not only to Robotics, but also to Biomechanics, Biomimmetics, Cybernetics, among other areas. This book presents a series of researches inspired by this ideal, carried through by various researchers worldwide, looking for to analyze and to discuss diverse subjects related to humanoid robots. The presented contributions explore aspects about robotic hands, learning, language, vision and locomotion

From locomotion to cognition: Bridging the gap between reactive and cognitive behavior in a quadruped robot

The cognitivistic paradigm, which states that cognition is a result of computation with symbols that represent the world, has been challenged by many. The opponents have primarily criticized the detachment from direct interaction with the world and pointed to some fundamental problems (for instance the symbol grounding problem). Instead, they emphasized the constitutive role of embodied interaction with the environment. This has motivated the advancement of synthetic methodologies: the phenomenon of interest (cognition) can be studied by building and investigating whole brain-body-environment systems. Our work is centered around a compliant quadruped robot equipped with a multimodal sensory set. In a series of case studies, we investigate the structure of the sensorimotor space that the application of different actions in different environments by the robot brings about. Then, we study how the agent can autonomously abstract the regularities that are induced by the different conditions and use them to improve its behavior. The agent is engaged in path integration, terrain discrimination and gait adaptation, and moving target following tasks. The nature of the tasks forces the robot to leave the ``here-and-now'' time scale of simple reactive stimulus-response behaviors and to learn from its experience, thus creating a ``minimally cognitive'' setting. Solutions to these problems are developed by the agent in a bottom-up fashion. The complete scenarios are then used to illuminate the concepts that are believed to lie at the basis of cognition: sensorimotor contingencies, body schema, and forward internal models. Finally, we discuss how the presented solutions are relevant for applications in robotics, in particular in the area of autonomous model acquisition and adaptation, and, in mobile robots, in dead reckoning and traversability detection

Understanding the fundamentals of bipedal locomotion in humans and robots

Walking is a robust and efficient method of moving around the world, which would greatly enhance the capabilities of humanoid robots, although they cannot match the performance of their biological counterparts. The highly nonlinear dynamics of locomotion create a vast state-action space, which makes model-based control difficult, yet biological humans are highly proficient and robust in their motion while operating under similar constraints. This disparity in performance naturally leads to the question: what can we learn about locomotion control by observing humans, and how can this be used to develop bio-inspired locomotion control in mechatronic humanoids? This thesis investigates bio-inspired locomotion control, but also explores the limitations of this approach and how we can use robotic platforms to move towards a better understanding of locomotion. We first present a methodology for measuring and analysing human locomotion behaviour, specifically disturbance recovery, and fit models to this complex behaviour to represent it in as simple as possible such that it can be easily translated into a simple controller for reactive motion. A minimum-jerk Model Predictive Control algorithm at the Centre of Mass (CoM) best captured human motion during multiple recovery strategies instead of using one controller for each strategy, which is common in this area. Capturing this simple CoM model of complex human behaviour shows that bio-inspiration can be an important tool for controller development, but behaviour varies between and even within individuals given similar initial conditions, which manifests as stochastic behaviour. Coupled with the ability to only measure expressed behaviours instead of direct control policies, this stochasticity presents a fundamental limit to using bio-inspiration for control purposes, as only indirect inferences can be made about a complex, stochastic system. To overcome these barriers, we investigate the use of mechatronic humanoid robots as a means to explore invariant aspects of the vast dynamic state-space of locomotion which are described by physical laws, and are therefore not subject to the stochastic behaviour of individual humans, that apply to both biological and mechatronic humanoid forms. We present a pipeline to explore the invariant energetics of humanoid robots during stepping for push recovery, where the most efficient stepping parameters are identified for a given initial CoM velocity and desired step length. Using this to explore the stepping state-space, our analysis finds a region of attraction between disturbance magnitude and optimal step length surrounded by a region of similarly efficient alternatives which corresponds to the stochastic behavior observed in humans during push recovery, which we would be unable to identify without reproducibility, direct access to internal measurements and known full body dynamics, which is not available in humans. We expand this paradigm further to investigate the invariant energetics of continuous walking using a full-body humanoid by exploring the state-space of step-length and step-timing to identify the most efficient sub-spaces of these parameters which describes the most efficient way to walk. Through analysis of this state-space, we provide evidence that the humanoid morphology exhibits a passive tendency towards energy-optimal motion and its dynamics follow a region of attraction towards Cost of Transport-optimal motion. Overall, these findings demonstrate the utility of robotics as a tool with which to explore certain aspects of legged locomotion and the results gained from our methodology suggest that humans do not need to explore a vast state-action space to learn to walk, they need only internalise simple heuristics for the natural dynamics of stepping that are easy to learn and can produce rapid, reactive and efficient stepping without costly decision-making processes

Design of artificial neural oscillatory circuits for the control of lamprey- and salamander-like locomotion using evolutionary algorithms

This dissertation investigates the evolutionary design of oscillatory artificial neural networks for the control of animal-like locomotion. It is inspired by the neural organ¬ isation of locomotor circuitries in vertebrates, and explores in particular the control of undulatory swimming and walking. The difficulty with designing such controllers is to find mechanisms which can transform commands concerning the direction and the speed of motion into the multiple rhythmic signals sent to the multiple actuators typically involved in animal-like locomotion. In vertebrates, such control mechanisms are provided by central pattern generators which are neural circuits capable of pro¬ ducing the patterns of oscillations necessary for locomotion without oscillatory input from higher control centres or from sensory feedback. This thesis explores the space of possible neural configurations for the control of undulatory locomotion, and addresses the problem of how biologically plausible neural controllers can be automatically generated.Evolutionary algorithms are used to design connectionist models of central pattern generators for the motion of simulated lampreys and salamanders. This work is inspired by Ekeberg's neuronal and mechanical simulation of the lamprey [Ekeberg 93]. The first part of the thesis consists of developing alternative neural controllers for a similar mechanical simulation. Using a genetic algorithm and an incremental approach, a variety of controllers other than the biological configuration are successfully developed which can control swimming with at least the same efficiency. The same method is then used to generate synaptic weights for a controller which has the observed biological connectivity in order to illustrate how the genetic algorithm could be used for developing neurobiological models. Biologically plausible controllers are evolved which better fit physiological observations than Ekeberg's hand-crafted model. Finally, in collaboration with Jerome Kodjabachian, swimming controllers are designed using a developmental encoding scheme, in which developmental programs are evolved which determine how neurons divide and get connected to each other on a two-dimensional substrate.The second part of this dissertation examines the control of salamander-like swimming and trotting. Salamanders swim like lampreys but, on the ground, they switch to a trotting gait in which the trunk performs a standing wave with the nodes at the girdles. Little is known about the locomotion circuitry of the salamander, but neurobiologists have hypothesised that it is based on a lamprey-like organisation. A mechanical sim¬ ulation of a salamander-like animat is developed, and neural controllers capable of exhibiting the two types of gaits are evolved. The controllers are made of two neural oscillators projecting to the limb motoneurons and to lamprey-like trunk circuitry. By modulating the tonic input applied to the networks, the type of gait, the speed and the direction of motion can be varied.By developing neural controllers for lamprey- and salamander-like locomotion, this thesis provides insights into the biological control of undulatory swimming and walking, and shows how evolutionary algorithms can be used for developing neurobiological models and for generating neural controllers for locomotion. Such a method could potentially be used for designing controllers for swimming or walking robots, for instance

Control of Bio-Inspired Sprawling Posture Quadruped Robots with an Actuated Spine

Sprawling posture robots are characterized by upper limb segments protruding horizontally from the body, resulting in lower body height and wider support on the ground. Combined with an actuated segmented spine and tail, such morphology resembles that of salamanders or crocodiles. Although bio-inspired salamander-like robots with simple rotational limbs have been created, not much research has been done on kinematically redundant bio-mimetic robots that can closely replicate kinematics of sprawling animal gaits. Being bio-mimetic could allow a robot to have some of the locomotion skills observed in those animals, expanding its potential applications in challenging scenarios. At the same time, the robot could be used to answer questions about the animal's locomotion. This thesis is focused on developing locomotion controllers for such robots. Due to their high number of degrees of freedom (DoF), the control is based on solving the limb and spine inverse kinematics to properly coordinate different body parts. It is demonstrated how active use of a spine improves the robot's walking and turning performance. Further performance improvement across a variety of gaits is achieved by using model predictive control (MPC) methods to dictate the motion of the robot's center of mass (CoM). The locomotion controller is reused on an another robot (OroBOT) with similar morphology, designed to mimic the kinematics of a fossil belonging to Orobates, an extinct early tetrapod. Being capable of generating different gaits and quantitatively measuring their characteristics, OroBOT was used to find the most probable way the animal moved. This is useful because understanding locomotion of extinct vertebrates helps to conceptualize major transitions in their evolution. To tackle field applications, e.g. in disaster response missions, a new generation of field-oriented sprawling posture robots was built. The robustness of their initial crocodile-inspired design was tested in the animal's natural habitat (Uganda, Africa) and subsequently enhanced with additional sensors, cameras and computer. The improvements to the software framework involved a smartphone user interface visualizing the robot's state and camera feed to improve the ease of use for the operator. Using force sensors, the locomotion controller is expanded with a set of reflex control modules. It is demonstrated how these modules improve the robot's performance on rough and unstructured terrain. The robot's design and its low profile allow it to traverse low passages. To also tackle narrow passages like pipes, an unconventional crawling gait is explored. While using it, the robot lies on the ground and pushes against the pipe walls to move the body. To achieve such a task, several new control and estimation modules were developed. By exploring these problems, this thesis illustrates fruitful interactions that can take place between robotics, biology and paleontology

Models, Simulations, and the Reduction of Complexity

Modern science is a model-building activity. But how are models contructed? How are they related to theories and data? How do they explain complex scientific phenomena, and which role do computer simulations play? To address these questions which are highly relevant to scientists as well as to philosophers of science, 8 leading natural, engineering and social scientists reflect upon their modeling work, and 8 philosophers provide a commentary