Stability analysis of snake robot locomotion based on Poincaré maps

Abstract — This paper presents an analysis of snake locomotion that explains how non-uniform viscous ground friction conditions enable snake robots to locomote forward on a planar surface. The explanation is based on a simple mapping from link velocities normal to the direction of motion into propulsive forces in the direction of motion. From this analysis, a controller for a snake robot is proposed. A Poincaré map is employed to prove that all state variables of the snake robot, except for the position in the forward direction, trace out an exponentially stable periodic orbit. I

Modeling, Control and Energy Efficiency of Underwater Snake Robots

This thesis is mainly motivated by the attribute of the snake robots that they are able to move over land as well as underwater while the physiology of the robot remains the same. This adaptability to different motion demands depending on the environment is one of the main characteristics of the snake robots. In particular, this thesis targets several interesting aspects regarding the modeling, control and energy efficiency of the underwater snake robots. This thesis addresses the problem of modeling the hydrodynamic effects with an analytical perspective and a primary objective to conclude in a closed-form solution for the dynamic model of an underwater snake robot. Two mathematical models of the kinematics and dynamics of underwater snake robots swimming in virtual horizontal and vertical planes aimed at control design are presented. The presented models are derived in a closed-form and can be utilized in modern modelbased control schemes. In addition, these proposed models comprise snake robots moving both on land and in water which makes the model applicable for unified control methods for amphibious snake robots moving both on land and in water. The third model presented in this thesis is based on simplifying assumptions in order to derive a control-oriented model of an underwater snake robot moving in a virtual horizontal plane that is well-suited for control design and stability analysis. The models are analysed using several techniques. An extensive analysis of the model of a fully immersed underwater snake robot moving in a virtual horizontal plane is conducted. Based on this analysis, a set of essential properties that characterize the overall motion of underwater snake robots is derived. An averaging analysis reveals new fundamental properties of underwater snake robot locomotion that are useful from a motion planning perspective. In this thesis, both the motion analysis and control strategies are conducted based on a general sinusoidal motion pattern which can be used for a broad class of motion patterns including lateral undulation and eel-like motion. This thesis proposes and experimentally validates solutions to the path following control problem for biologically inspired swimming snake robots. In particular, line-of-sight (LOS) and integral line-of-sight (I-LOS) guidance laws, which are combined with a sinusoidal gait pattern and a directional controller that steers the robot towards and along the desired path are proposed. An I-LOS path following controller for steering an underwater snake robot along a straight line path in the presence of ocean currents of unknown direction and magnitude is presented and by using a Poincaré map, it is shown that all state variables of an underwater snake robot, except for the position along the desired path, trace out an exponentially stable periodic orbit. Moreover, this thesis presents the combined use of an artificial potential fields-based path planner with a new waypoint guidance strategy for steering an underwater snake robot along a path defined by waypoints interconnected by straight lines. The waypoints are derived by using a path planner based on the artificial potential field method in order to also address the obstacle avoidance problem. Furthermore, this thesis considers the energy efficiency of underwater snake robots. In particular, the relationship between the parameters of the gait patterns, the forward velocity and the energy consumption for the different motion patterns for underwater snake robots is investigated. Based on simulation results, this thesis presents empirical rules to choose the values for the parameters of the motion gait pattern of underwater snake robots. The experimental results support the derived properties regarding the relationship between the gait parameters and the power consumption both for lateral undulation and eel-like motion patterns. Moreover, comparison results are obtained for the total energy consumption and the cost of transportation of underwater snake robots and remotely operated vehicles (ROVs). Furthermore, in this thesis a multi-objective optimization problem is developed with the aim of maximizing the achieved forward velocity of the robot and minimizing the corresponding average power consumption of the system

Novel Locomotion Methods in Magnetic Actuation and Pipe Inspection

There is much room for improvement in tube network inspections of jet aircraft. Often, these inspections are incomplete and inconsistent. In this paper, we develop a Modular Robotic Inspection System (MoRIS) for jet aircraft tube networks and a corresponding kinematic model. MoRIS consists of a Base Station for user control and communication, and robotic Vertebrae for accessing and inspecting the network. The presented and tested design of MoRIS can travel up to 9 feet in a tube network. The Vertebrae can navigate in all orientations, including smooth vertical tubes. The design is optimized for nominal 1.5 outside diameter tubes. We developed a model of the Locomotion Vertebra in a tube. We defined the model\u27s coordinate system and its generalized coordinates. We studied the configuration space of the robot, which includes all possible orientations of the Locomotion Vertebra. We derived the expression for the elastic potential energy of the Vertebra\u27s suspensions and minimized it to find the natural settling orientation of the robot. We further explore the effect of the tractive wheel\u27s velocity constraint on locomotion dynamics. Finally, we develop a general model for aircraft tube networks and for a taut tether. Stabilizing bipedal walkers is a engineering target throughout the research community. In this paper, we develop an impulsively actuated walking robot. Through the use of magnetic actuation, for the first time, pure impulsive actuation has been achieved in bipedal walkers. In studying this locomotion technique, we built the world\u27s smallest walker: Big Foot. A dynamical model was developed for Big Foot. A Heel Strike and a Constant Pulse Wave Actuation Schemes were selected for testing. The schemes were validated through simulations and experiments. We showed that there exists two regimes for impulsive actuation. There is a regime for impact-like actuation and a regime for longer duration impulsive actuation

Bio-inspired robotic control in underactuation: principles for energy efficacy, dynamic compliance interactions and adaptability.

Biological systems achieve energy efficient and adaptive behaviours through extensive autologous and exogenous compliant interactions. Active dynamic compliances are created and enhanced from musculoskeletal system (joint-space) to external environment (task-space) amongst the underactuated motions. Underactuated systems with viscoelastic property are similar to these biological systems, in that their self-organisation and overall tasks must be achieved by coordinating the subsystems and dynamically interacting with the environment. One important question to raise is: How can we design control systems to achieve efficient locomotion, while adapt to dynamic conditions as the living systems do? In this thesis, a trajectory planning algorithm is developed for underactuated microrobotic systems with bio-inspired self-propulsion and viscoelastic property to achieve synchronized motion in an energy efficient, adaptive and analysable manner. The geometry of the state space of the systems is explicitly utilized, such that a synchronization of the generalized coordinates is achieved in terms of geometric relations along the desired motion trajectory. As a result, the internal dynamics complexity is sufficiently reduced, the dynamic couplings are explicitly characterised, and then the underactuated dynamics are projected onto a hyper-manifold. Following such a reduction and characterization, we arrive at mappings of system compliance and integrable second-order dynamics with the passive degrees of freedom. As such, the issue of trajectory planning is converted into convenient nonlinear geometric analysis and optimal trajectory parameterization. Solutions of the reduced dynamics and the geometric relations can be obtained through an optimal motion trajectory generator. Theoretical background of the proposed approach is presented with rigorous analysis and developed in detail for a particular example. Experimental studies are conducted to verify the effectiveness of the proposed method. Towards compliance interactions with the environment, accurate modelling or prediction of nonlinear friction forces is a nontrivial whilst challenging task. Frictional instabilities are typically required to be eliminated or compensated through efficiently designed controllers. In this work, a prediction and analysis framework is designed for the self-propelled vibro-driven system, whose locomotion greatly relies on the dynamic interactions with the nonlinear frictions. This thesis proposes a combined physics-based and analytical-based approach, in a manner that non-reversible characteristic for static friction, presliding as well as pure sliding regimes are revealed, and the frictional limit boundaries are identified. Nonlinear dynamic analysis and simulation results demonstrate good captions of experimentally observed frictional characteristics, quenching of friction-induced vibrations and satisfaction of energy requirements. The thesis also performs elaborative studies on trajectory tracking. Control schemes are designed and extended for a class of underactuated systems with concrete considerations on uncertainties and disturbances. They include a collocated partial feedback control scheme, and an adaptive variable structure control scheme with an elaborately designed auxiliary control variable. Generically, adaptive control schemes using neural networks are designed to ensure trajectory tracking. Theoretical background of these methods is presented with rigorous analysis and developed in detail for particular examples. The schemes promote the utilization of linear filters in the control input to improve the system robustness. Asymptotic stability and convergence of time-varying reference trajectories for the system dynamics are shown by means of Lyapunov synthesis

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

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. [...

Physics-based Machine Learning Methods for Control and Sensing in Fish-like Robots

Underwater robots are important for the construction and maintenance of underwater infrastructure, underwater resource extraction, and defense. However, they currently fall far behind biological swimmers such as fish in agility, efficiency, and sensing capabilities. As a result, mimicking the capabilities of biological swimmers has become an area of significant research interest. In this work, we focus specifically on improving the control and sensing capabilities of fish-like robots. Our control work focuses on using the Chaplygin sleigh, a two-dimensional nonholonomic system which has been used to model fish-like swimming, as part of a curriculum to train a reinforcement learning agent to control a fish-like robot to track a prescribed path. The agent is first trained on the Chaplygin sleigh model, which is not an accurate model of the swimming robot but crucially has similar physics; having learned these physics, the agent is then trained on a simulated swimming robot, resulting in faster convergence compared to only training on the simulated swimming robot. Our sensing work separately considers using kinematic data (proprioceptive sensing) and using surface pressure sensors. The effect of a swimming body\u27s internal dynamics on proprioceptive sensing is investigated by collecting time series of kinematic data of both a flexible and rigid body in a water tunnel behind a moving obstacle performing different motions, and using machine learning to classify the motion of the upstream obstacle. This revealed that the flexible body could more effectively classify the motion of the obstacle, even if only one if its internal states is used. We also consider the problem of using time series data from a `lateral line\u27 of pressure sensors on a fish-like body to estimate the position of an upstream obstacle. Feature extraction from the pressure data is attempted with a state-of-the-art convolutional neural network (CNN), and this is compared with using the dominant modes of a Koopman operator constructed on the data as features. It is found that both sets of features achieve similar estimation performance using a dense neural network to perform the estimation. This highlights the potential of the Koopman modes as an interpretable alternative to CNNs for high-dimensional time series. This problem is also extended to inferring the time evolution of the flow field surrounding the body using the same surface measurements, which is performed by first estimating the dominant Koopman modes of the surrounding flow, and using those modes to perform a flow reconstruction. This strategy of mapping from surface to field modes is more interpretable than directly constructing a mapping of unsteady fluid states, and is found to be effective at reconstructing the flow. The sensing frameworks developed as a result of this work allow better awareness of obstacles and flow patterns, knowledge which can inform the generation of paths through the fluid that the developed controller can track, contributing to the autonomy of swimming robots in challenging environments

Engineering Dynamics and Life Sciences

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

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

Models for reinforcement learning and design of a soft robot inspired by Drosophila larvae

Designs for robots are often inspired by animals, as they are designed mimicking animals’ mechanics, motions, behaviours and learning. The Drosophila, known as the fruit fly, is a well-studied model animal. In this thesis, the Drosophila larva is studied and the results are applied to robots. More specifically: a part of the Drosophila larva’s neural circuit for operant learning is modelled, based on which a synaptic plasticity model and a neural circuit model for operant learning, as well as a dynamic neural network for robot reinforcement learning, are developed; then Drosophila larva’s motor system for locomotion is studied, and based on it a soft robot system is designed. Operant learning is a concept similar to reinforcement learning in computer science, i.e. learning by reward or punishment for behaviour. Experiments have shown that a wide range of animals is capable of operant learning, including animal with only a few neurons, such as Drosophila. The fact implies that operant learning can establish without a large number of neurons. With it as an assumption, the structure and dynamics of synapses are investigated, and a synaptic plasticity model is proposed. The model includes nonlinear dynamics of synapses, especially receptor trafficking which affects synaptic strength. Tests of this model show it can enable operant learning at the neuron level and apply to a broad range of NNs, including feedforward, recurrent and spiking NNs. The mushroom body is a learning centre of the insect brain known and modelled for associative learning, but not yet for operant learning. To investigate whether it participates in operant learning, Drosophila larvae are studied with a transgenic tool by my collaborators. Based on the experiment and the results, a mushroom body model capable of operant learning is modelled. The proposed neural circuit model can reproduce the operant learning of the turning behaviour of Drosophila larvae. Then the synaptic plasticity model is simplified for robot learning. With the simplified model, a recurrent neural network with internal neural dynamics can learn to control a planar bipedal robot in a benchmark reinforcement learning task which is called bipedal walker by OpenAI. Benefiting efficiency in parameter space exploration instead of action space exploration, it is the first known solution to the task with reinforcement learning approaches. Although existing pneumatic soft robots can have multiple muscles embedded in a component, it is far less than the muscles in the Drosophila larva, which are well-organised in a tiny space. A soft robot system is developed based on the muscle pattern of the Drosophila larva, to explore the possibility to embed a high density of muscles in a limited space. Three versions of the body wall with pneumatic muscles mimicking the muscle pattern are designed. A pneumatic control system and embedded control system are also developed for controlling the robot. With a bioinspired body wall will a large number of muscles, the robot performs lifelike motions in experiments