Dynamics and Control of Nonholonomic Systems with Internal Degrees of Freedom

Nonholonomic systems model many robots as well as animals and other systems. Although such systems have been studied extensively over the last century, much work still remains to be done on their dynamics and control. Many techniques have been developed for controlling kinematic nonholonomic systems or simplified dynamic versions, however control of high dimensional, underactuated nonholonomic systems remains to be addressed. This dissertation helps fill this gap by developing a control algorithm that can be applied to systems with three or more configuration variables and just one input. We also analyze the dynamic effects of passive degrees of freedom and elastic potentials which are commonly observed in such systems showing that the addition of a passive degree of freedom can even be used to improve the locomotion characteristics of a system. Such elastic potentials can be present due to compliant mechanisms or origami, both of which can exhibit bistability and many other properties that can be useful in the design of robots

Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Includes bibliographical references (leaves 308-316).This thesis is devoted to nonlinear control, reduction, and classification of underactuated mechanical systems. Underactuated systems are mechanical control systems with fewer controls than the number of configuration variables. Control of underactuated systems is currently an active field of research due to their broad applications in Robotics, Aerospace Vehicles, and Marine Vehicles. The examples of underactuated systems include flexible-link robots, nobile robots, walking robots, robots on mobile platforms, cars, locomotive systems, snake-type and swimming robots, acrobatic robots, aircraft, spacecraft, helicopters, satellites, surface vessels, and underwater vehicles. Based on recent surveys, control of general underactuated systems is a major open problem. Almost all real-life mechanical systems possess kinetic symmetry properties, i.e. their kinetic energy does not depend on a subset of configuration variables called external variables. In this work, I exploit such symmetry properties as a means of reducing the complexity of control design for underactuated systems. As a result, reduction and nonlinear control of high-order underactuated systems with kinetic symmetry is the main focus of this thesis. By "reduction", we mean a procedure to reduce control design for the original underactuated system to control of a lowerorder nonlinear or mechanical system. One way to achieve such a reduction is by transforming an underactuated system to a cascade nonlinear system with structural properties. If all underactuated systems in a class can be transformed into a specific class of nonlinear systems, we refer to the transformed systems as the "normal form" of the corresponding class of underactuated systems. Our main contribution is to find explicit change of coordinates and control that transform several classes of underactuated systems, which appear in robotics and aerospace applications, into cascade nonlinear systems with structural properties that are convenient for control design purposes. The obtained cascade normal forms are three classes of nonlinear systems, namely, systems in strict feedback form, feedforward form, and nontriangular linear-quadratic form. The names of these three classes are due to the particular lower-triangular, upper-triangular, and nontriangular structure in which the state variables appear in the dynamics of the corresponding nonlinear systems. The triangular normal forms of underactuated systems can be controlled using existing backstepping and feedforwarding procedures. However, control of the nontriangular normal forms is a major open problem. We address this problem for important classes of nontriangular systems of interest by introducing a new stabilization method based on the solutions of fixed-point equations as stabilizing nonlinear state feedback laws. This controller is obtained via a simple recursive method that is convenient for implementation. For special classes of nontriangular nonlinear systems, such fixed-point equations can be solved explicitly ...by Reza Olfati-Saber.Ph.D

Perception Based Navigation for Underactuated Robots.

Robot autonomous navigation is a very active field of robotics. In this thesis we propose a hierarchical approach to a class of underactuated robots by composing a collection of local controllers with well understood domains of attraction. We start by addressing the problem of robot navigation with nonholonomic motion constraints and perceptual cues arising from onboard visual servoing in partially engineered environments. We propose a general hybrid procedure that adapts to the constrained motion setting the standard feedback controller arising from a navigation function in the fully actuated case. This is accomplished by switching back and forth between moving "down" and "across" the associated gradient field toward the stable manifold it induces in the constrained dynamics. Guaranteed to avoid obstacles in all cases, we provide conditions under which the new procedure brings initial configurations to within an arbitrarily small neighborhood of the goal. We summarize with simulation results on a sample of visual servoing problems with a few different perceptual models. We document the empirical effectiveness of the proposed algorithm by reporting the results of its application to outdoor autonomous visual registration experiments with the robot RHex guided by engineered beacons. Next we explore the possibility of adapting the resulting first order hybrid feedback controller to its dynamical counterpart by introducing tunable damping terms in the control law. Just as gradient controllers for standard quasi-static mechanical systems give rise to generalized "PD-style" controllers for dynamical versions of those standard systems, we show that it is possible to construct similar "lifts" in the presence of non-holonomic constraints notwithstanding the necessary absence of point attractors. Simulation results corroborate the proposed lift. Finally we present an implementation of a fully autonomous navigation application for a legged robot. The robot adapts its leg trajectory parameters by recourse to a discrete gradient descent algorithm, while managing its experiments and outcome measurements autonomously via the navigation visual servoing algorithms proposed in this thesis.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/58412/1/glopes_1.pd

분산된 로터로 구동되는 비행 스켈레톤 시스템의 디자인 상태추정 및 제어

학위논문(박사)--서울대학교 대학원 :공과대학 기계항공공학부,2020. 2. 이동준.In this thesis, we present key theoretical components for realizing flying aerial skeleton system called LASDRA (large-size aerial skeleton with distributed rotor actuation). Aerial skeletons are articulated aerial robots actuated by distributed rotors including both ground connected type and flying type. These systems have recently attracted interest and are being actively researched in several research groups, with the expectation of applying those for aerial manipulation in distant/narrow places, or for the performance with entertaining purpose such as drone shows. Among the aerial skeleton systems, LASDRA system, proposed by our group has some significant advantages over the other skeleton systems that it is capable of free SE(3) motion by omni-directional wrench generation of each link, and also the system can be operated with wide range of configuration because of the 3DOF (degrees of freedom) inter-link rotation enabled by cable connection among the link modules. To realize this LASDRA system, following three components are crucial: 1) a link module that can produce omni-directional force and torque and enough feasible wrench space; 2) pose and posture estimation algorithm for an articulated system with high degrees of freedom; and 3) a motion generation framework that can provide seemingly natural motion while being able to generate desired motion (e.g., linear and angular velocity) for the entire body. The main contributions of this thesis is theoretically developing these three components, and verifying these through outdoor flight experiment with a real LASDRA system. First of all, a link module for the LASDRA system is designed with proposed constrained optimization problem, maximizing the guaranteed feasible force and torque for any direction while also incorporating some constraints (e.g., avoiding inter-rotor air-flow interference) to directly obtain feasible solution. Also, an issue of ESC-induced (electronic speed control) singularity is first introduced in the literature which is inevitably caused by bi-directional thrust generation with sensorless actuators, and handled with a novel control allocation called selective mapping. Then for the state estimation of the entire LASDRA system, constrained Kalman filter based estimation algorithm is proposed that can provide estimation result satisfying kinematic constraint of the system, also along with a semi-distributed version of the algorithm to endow with system scalability. Lastly, CPG-based motion generation framework is presented that can generate natural biomimetic motion, and by exploiting the inverse CPG model obtained with machine learning method, it becomes possible to generate certain desired motion while still making CPG generated natural motion.본 논문에서는 비행 스켈레톤 시스템 LASDRA (large-size aerial skeleton with distributed rotor actuation) 의 구현을 위해 요구되는 핵심 기법들을 제안하며, 이를 실제 LASDRA 시스템의 실외 비행을 통해 검증한다. 제안된 기법은 1) 전방향으로 힘과 토크를 낼 수 있고 충분한 가용 렌치공간을 가진 링크 모듈, 2) 높은 자유도의 다관절구조 시스템을 위한 위치 및 자세 추정 알고리즘, 3) 자연스러운 움직임을 내는 동시에 전체 시스템이 속도, 각속도 등 원하는 움직임을 내도록 할 수 있는 모션 생성 프레임워크로 구성된다. 본 논문에서는 우선 링크 모듈의 디자인을 위해 전방향으로 보장되는 힘과 토크의 크기를 최대화하는 구속 최적화를 사용하고, 실제 적용가능한 해를 얻기 위해 몇가지 구속조건(로터 간 공기 흐름 간섭의 회피 등)을 고려한다. 또한 센서가 없는 액츄에이터로 양방향 추력을 내는 것에서 야기되는 ESC 유발 특이점 (ESC-induced singularity) 이라는 문제를 처음으로 소개하고, 이를 해결하기 위해 선택적 맵핑 (selective mapping) 이라는 기법을 제시한다. 전체 LASDRA 시스템의 상태추정을 위해 시스템의 기구학적 구속조건을 만족하는 결과를 얻을 수 있도록 구속 칼만 필터 기반의 상태추정 기법을 제시하고, 시스템 확장성을 고려하여 반 분산 (semi-distributed) 개념의 알고리즘을 함께 제시한다. 마지막으로 본 논문에서는 자연스러운 움직임의 생성을 위하여 CPG 기반의 모션 생성 프레임워크를 제안하며, 기계 학습 방법을 통해 CPG 역연산 모델을 얻음으로써 전체 시스템이 원하는 움직임을 낼 수 있도록 한다.1 Introduction 1 1.1 Motivation and Background 1 1.2 Research Problems and Approach 3 1.3 Preview of Contributions 5 2 Omni-Directional Aerial Robot 7 2.1 Introduction 7 2.2 Mechanical Design 12 2.2.1 Design Description 12 2.2.2 Wrench-Maximizing Design Optimization 13 2.3 System Modeling and Control Design 20 2.3.1 System Modeling 20 2.3.2 Pose Trajectory Tracking Control 22 2.3.3 Hybrid Pose/Wrench Control 22 2.3.4 PSPM-Based Teleoperation 24 2.4 Control Allocation with Selective Mapping 27 2.4.1 Infinity-Norm Minimization 27 2.4.2 ESC-Induced Singularity and Selective Mapping 29 2.5 Experiment 38 2.5.1 System Setup 38 2.5.2 Experiment Results 41 2.6 Conclusion 49 3 Pose and Posture Estimation of an Aerial Skeleton System 51 3.1 Introduction 51 3.2 Preliminary 53 3.3 Pose and Posture Estimation 55 3.3.1 Estimation Algorithm via SCKF 55 3.3.2 Semi-Distributed Version of Algorithm 59 3.4 Simulation 62 3.5 Experiment 65 3.5.1 System Setup 65 3.5.2 Experiment of SCKF-Based Estimation Algorithm 66 3.6 Conclusion 69 4 CPG-Based Motion Generation 71 4.1 Introduction 71 4.2 Description of Entire Framework 75 4.2.1 LASDRA System 75 4.2.2 Snake-Like Robot & Pivotboard 77 4.3 CPG Model 79 4.3.1 LASDRA System 79 4.3.2 Snake-Like Robot 80 4.3.3 Pivotboard 83 4.4 Target Pose Calculation with Expected Physics 84 4.5 Inverse Model Learning 86 4.5.1 LASDRA System 86 4.5.2 Snake-Like Robot 89 4.5.3 Pivotboard 90 4.6 CPG Parameter Adaptation 93 4.7 Simulation 94 4.7.1 LASDRA System 94 4.7.2 Snake-Like Robot & Pivotboard 97 4.8 Conclusion 101 5 Outdoor Flight Experiment of the F-LASDRA System 103 5.1 System Setup 103 5.2 Experiment Results 104 6 Conclusion 111 6.1 Summary 111 6.2 Future Works 112Docto

Motion Planning for Underactuated Systems through Path Parameterisation

Underactuated systems are becoming an essential field of study within robotics given the rapid advancement and prevalence of legged and flying systems within the modern world. Planning motions that are dynamically feasible for these systems is integral to achieving natural and dynamic movement, however, a great difficulty posed by underactuation is that the space of feasible motions for these systems is strongly constrained by their dynamics. This thesis investigates the viability of extending path-parameterised motion planning to underactuated systems, where algorithms are proposed in two key areas, sample-based and optimisation-based planning. A focus is placed on systems with a single degree of underactuation, where the scalar dynamics revealed under a path parameterisation can be used for efficient kinodynamic querying and dynamic feasibility verification of generated paths. Within a sample-based context, these features are exploited through the development of a path-parameterised RRT algorithm with a state-based steering strategy that accommodates this degree of underactuation. Within the numerical optimisation front, these features are used to develop a path-parameterised trajectory optimisation method with dynamic feasibility detection, enabling the rapid generation of feasible motions with fine dynamical accuracy. This work demonstrates the advantages of these algorithms in relation to existing approaches, highlighting the successes attributed to the exploitation of this class of underactuated system under a path parameterisation

Control of multiple model systems

This thesis considers the control of multiple model systems. These are systems for which only one model out of some finite set of models gives the system dynamics at any given time. In particular, the model that gives the system dynamics can change over time. This thesis covers some of the theoretical aspects of these systems, including controllability and stabilizability. As an application, ``overconstrained' mechanical systems are modeled as multiple model systems. Examples of such systems include distributed manipulation problems such as microelectromechanical systems and many wheeled vehicles such as the Sojourner vehicle of the Mars Pathfinder mission. Such systems are typified by having more Pfaffian constraints than degrees of freedom. Conventional classical motion planning and control theories do not directly apply to overconstrained systems. Control issues for two examples are specifically addressed. The first example is distributed manipulation. Distributed manipulation systems control an object's motion through contact with a high number of actuators. Stability results are shown for such systems and control schemes based on these results are implemented on a distributed manipulation test-bed. The second example is that of overconstrained vehicles, of which the Mars rover is an example. The nonlinear controllability test for multiple model systems is used to answer whether a kinematic model of the rover is or is not controllable

Data-Driven Methods to Build Robust Legged Robots

For robots to ever achieve signicant autonomy, they need to be able to mitigate performance loss due to uncertainty, typically from a novel environment or morphological variation of their bodies. Legged robots, with their complex dynamics, are particularly challenging to control with principled theory. Hybrid events, uncertainty, and high dimension are all confounding factors for direct analysis of models. On the other hand, direct data-driven methods have proven to be equally dicult to employ. The high dimension and mechanical complexity of legged robots have proven challenging for hardware-in-the-loop strategies to exploit without signicant eort by human operators. We advocate that we can exploit both perspectives by capitalizing on qualitative features of mathematical models applicable to legged robots, and use that knowledge to strongly inform data-driven methods. We show that the existence of these simple structures can greatly facilitate robust design of legged robots from a data-driven perspective. We begin by demonstrating that the factorial complexity of hybrid models can be elegantly resolved with computationally tractable algorithms, and establish that a novel form of distributed control is predicted. We then continue by demonstrating that a relaxed version of the famous templates and anchors hypothesis can be used to encode performance objectives in a highly redundant way, allowing robots that have suffered damage to autonomously compensate. We conclude with a deadbeat stabilization result that is quite general, and can be determined without equations of motion.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155053/1/gcouncil_1.pd