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

Optimized adaptive tracking control for an underactuated vibro-driven capsule system

This paper studies the issue of adaptive trajectory tracking control for an underactuated vibro-driven capsule system and presents a novel motion generation framework. In this framework, feasible motion trajectory is derived through investigating dynamic constraints and kernel control indexes that underlie the underactuated dynamics. Due to the underactuated nature of the capsule system, the global motion dynamics cannot be directly controlled. The main objective of optimization is to indirectly control the friction-induced stick–slip motions to reshape the passive dynamics and, by doing so, to obtain optimal system performance in terms of average speed and energy efficacy. Two tracking control schemes are designed using a closed-loop feedback linearization approach and an adaptive variable structure control method with an auxiliary control variable, respectively. The reference model is accurately matched in a finite-time horizon. The key point is to define an exogenous state variable whose dynamics is employed as a control input. The tracking performance and system stability are investigated through rigorous theoretic analysis. Extensive simulation studies are conducted to demonstrate the effectiveness and feasibility of the developed trajectory model and optimized adaptive control system

Contributions to ida-pbc with adaptive control for underactuated mechanical systems

This master thesis is devoted to developing an adaptive control scheme for the well- known Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) technique. The main objective of this adaptive scheme is to asymptotically stabilize a class of Underactuated Mechanical Systems (UMSs) in the presence of uncertainties (not necessarily matched). This class of UMSs is characterized by the solvability of the Partial Differential Equation (PDE) resulting from the IDA-PBC technique. Two propositions are stated in this work to design the adaptive IDA-PBC. One of the main properties of these propositions is that even though the parameter estimation conver- gence is not guaranteed, the adaptive IDA-PBC achieves asymptotic stabilization. To illustrate the effectiveness of these propositions, this work performs simulations of the Inertia Wheel Inverted Pendulum (IWIP) system, considering a time-dependent input disturbance, a type of physical damping, i.e., friction (not considered in the standard IDA-PBC methodology), and parameter uncertainties in the system (e.g., inertia).Tesi

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

Adaptive Sliding Mode Control of Mobile Manipulators with Markovian Switching Joints

The hybrid joints of manipulators can be switched to either active (actuated) or passive (underactuated) mode as needed. Consider the property of hybrid joints, the system switches stochastically between active and passive systems, and the dynamics of the jump system cannot stay on each trajectory errors region of subsystems forever; therefore, it is difficult to determine whether the closed-loop system is stochastically stable. In this paper, we consider stochastic stability and sliding mode control for mobile manipulators using stochastic jumps switching joints. Adaptive parameter techniques are adopted to cope with the effect of Markovian switching and nonlinear dynamics uncertainty and follow the desired trajectory for wheeled mobile manipulators. The resulting closed-loop system is bounded in probability and the effect due to the external disturbance on the tracking errors can be attenuated to any preassigned level. It has been shown that the adaptive control problem for the Markovian jump nonlinear systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. Finally, a numerical example is given to show the potential of the proposed techniques

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

Metastable legged-robot locomotion

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 195-215).A variety of impressive approaches to legged locomotion exist; however, the science of legged robotics is still far from demonstrating a solution which performs with a level of flexibility, reliability and careful foot placement that would enable practical locomotion on the variety of rough and intermittent terrain humans negotiate with ease on a regular basis. In this thesis, we strive toward this particular goal by developing a methodology for designing control algorithms for moving a legged robot across such terrain in a qualitatively satisfying manner, without falling down very often. We feel the definition of a meaningful metric for legged locomotion is a useful goal in and of itself. Specifically, the mean first-passage time (MFPT), also called the mean time to failure (MTTF), is an intuitively practical cost function to optimize for a legged robot, and we present the reader with a systematic, mathematical process for obtaining estimates of this MFPT metric. Of particular significance, our models of walking on stochastically rough terrain generally result in dynamics with a fast mixing time, where initial conditions are largely "forgotten" within 1 to 3 steps. Additionally, we can often find a near-optimal solution for motion planning using only a short time-horizon look-ahead. Although we openly recognize that there are important classes of optimization problems for which long-term planning is required to avoid "running into a dead end" (or off of a cliff!), we demonstrate that many classes of rough terrain can in fact be successfully negotiated with a surprisingly high level of long-term reliability by selecting the short-sighted motion with the greatest probability of success. The methods used throughout have direct relevance to machine learning, providing a physics-based approach to reduce state space dimensionality and mathematical tools to obtain a scalar metric quantifying performance of the resulting reduced-order system.by Katie Byl.Ph.D

Modeling and adaptive tracking for stochastic nonholonomic constrained mechanical systems

This paper is devoted to the problem of modeling and trajectory tracking for stochastic nonholonomic dynamic systems in the presence of unknown parameters. Prior to tracking controller design, the rigorous derivation of stochastic nonholonomic dynamic model is given. By reasonably introducing so-called internal state vector, a reduced dynamic model, which is suitable for control design, is proposed. Based on the backstepping technique in vector form, an adaptive tracking controller is then derived, guaranteeing that the mean square of the tracking error converges to an arbitrarily small neighborhood of zero by tuning design parameters. The efficiency of the controller is demonstrated by a mechanics system: a vertical mobile wheel in random vibration environment

Optimal control of an underactuated bipedal robot

Bipedal robots represent a unique class of control problems that combine many of the most difficult elements of nonlinear control. These robots are typically designed to be mobile and as such have limited energy and actuator authority making efficiency a prime concern. Unlike wheeled robots, legged robots must transition between different equations of motion as legs make and break contact with the ground, aggravating the complexities of hybrid dynamics. Furthermore, small feet and series elastic actuation of joints leads to an underactuated system, causing traditional nonlinear control methods to struggle. This thesis describes and validates a general framework for efficiently controlling systems with the properties most problematic in bipedal robots, i.e., nonlinearity, hybrid dynamics, and underactuation. This process is two-step in that, first, an optimal trajectory is generated using direct collocation trajectory optimization, and second, the feasible trajectory is stabilized using a time varying linear quadratic regulator. We demonstrate this process on a number of toy problems including the triple pendulum on a cart and a reduced order template for a running robot. This approach is then applied to the bipedal robot ATRIAS in simulation in order to achieve efficient, dynamic, and robust locomotion behaviors