The Mechanics and Control of Undulatory Robotic Locomotion

In this dissertation, we examine a formulation of problems of undulatory robotic locomotion within the context of mechanical systems with nonholonomic constraints and symmetries. Using tools from geometric mechanics, we study the underlying structure found in general problems of locomotion. In doing so, we decompose locomotion into two basic components: internal shape changes and net changes in position and orientation. This decomposition has a natural mathematical interpretation in which the relationship between shape changes and locomotion can be described using a connection on a trivial principal fiber bundle. We begin by reviewing the processes of Lagrangian reduction and reconstruction for unconstrained mechanical systems with Lie group symmetries, and present new formulations of this process which are easily adapted to accommodate external constraints. Additionally, important physical quantities such as the mechanical connection and reduced mass-inertia matrix can be trivially determined using this formulation. The presence of symmetries then allows us to reduce the necessary calculations to simple matrix manipulations. The addition of constraints significantly complicates the reduction process; however, we show that for invariant constraints, a meaningful connection can be synthesized by defining a generalized momentum representing the momentum of the system in directions allowed by the constraints. We then prove that the generalized momentum and its governing equation possess certain invariances which allows for a reduction process similar to that found in the unconstrained case. The form of the reduced equations highlights the synthesized connection and the matrix quantities used to calculate these equations. The use of connections naturally leads to methods for testing controllability and aids in developing intuition regarding the generation of various locomotive gaits. We present accessibility and controllability tests based on taking derivatives of the connection, and relate these tests to taking Lie brackets of the input vector fields. The theory is illustrated using several examples, in particular the examples of the snakeboard and Hirose snake robot. We interpret each of these examples in light of the theory developed in this thesis, and examine the generation of locomotive gaits using sinusoidal inputs and their relationship to the controllability tests based on Lie brackets

Passivity-Based Trajectory Tracking and Formation Control of Nonholonomic Wheeled Robots Without Velocity Measurements

This note proposes a passivity-based control method for trajectory tracking and formation control of nonholonomic wheeled robots without velocity measurements. Coordinate transformations are used to incorporate the nonholonomic constraints, which are then avoided by controlling the front end of the robot rather than the center of the wheel axle into the differential equations. Starting from the passivity-based coordination design, the control goals are achieved via an internal controller for velocity tracking and heading control and an external controller for formation in the port-Hamiltonian framework. This approach endows the resulting controller with a physical interpretation. To avoid unavailable velocity measurements or unreliable velocity estimations, we derive the distributed control law with only position measurements by introducing a dynamic extension. In addition, we prove that our approach is suitable not only for acyclic graphs but also for a class of non-acyclic graphs, namely, ring graphs. Simulations are provided to illustrate the effectiveness of the approach

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

Control of mechanical systems on Lie groups based on vertically transverse functions

"The transverse function approach to control provides a unified setting to deal with practical stabilization and tracking of arbitrary trajectories for controllable driftless systems. Controllers derived from that approach offer advantages over those based on more classical techniques for control of nonholonomic systems. Nevertheless, its extension to more general classes, such as critical underactuated mechanical systems, is not immediate. The present paper explores a possible extension by developing a framework that allows one to cast point stabilization problems for (left-invariant) second-order systems on Lie groups, including simple mechanical systems. The approach is based on "vertical transversality," a property exhibited by derivatives of transverse functions. In this paper, we lay out the theoretical foundations of our approach and present an example to illustrate some of its features.

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

Efficient Reorientation Maneuvers for Spacecraft with Multiple Articulated Payloads

A final report is provided which describes the research program during the period 3 Mar. 1992 to 3 Jun. 1993. A summary of the technical research questions that were studied and of the main results that were obtained is given. The specific outcomes of the research program, including both educational impacts as well as research publications, are listed. The research is concerned with efficient reorientation maneuvers for spacecraft with multiple articulated payloads

Research on a semiautonomous mobile robot for loosely structured environments focused on transporting mail trolleys

In this thesis is presented a novel approach to model, control, and planning the motion of a nonholonomic wheeled mobile robot that applies stable pushes and pulls to a nonholonomic cart (York mail trolley) in a loosely structured environment. The method is based on grasping and ungrasping the nonholonomic cart, as a result, the robot changes its kinematics properties. In consequence, two robot configurations are produced by the task of grasping and ungrasping the load, they are: the single-robot configuration and the robot-trolley configuration. Furthermore, in order to comply with the general planar motion law of rigid bodies and the kinematic constraints imposed by the robot wheels for each configuration, the robot has been provided with two motorized steerable wheels in order to have a flexible platform able to adapt to these restrictions. [Continues.

Exponential Stabilization of Driftless Nonlinear Control Systems

This dissertation lays the foundation for practical exponential stabilization of driftless control systems. Driftless systems have the form, xdot = X1(x)u1 + .... + Xm(x)um, x ∈ ℝ^n Such systems arise when modeling mechanical systems with nonholonomic constraints. In engineering applications it is often required to maintain the mechanical system around a desired configuration. This task is treated as a stabilization problem where the desired configuration is made an asymptotically stable equilibrium point. The control design is carried out on an approximate system. The approximation process yields a nilpotent set of input vector fields which, in a special coordinate system, are homogeneous with respect to a non-standard dilation. Even though the approximation can be given a coordinate-free interpretation, the homogeneous structure is useful to exploit: the feedbacks are required to be homogeneous functions and thus preserve the homogeneous structure in the closed-loop system. The stability achieved is called p-exponential stability. The closed-loop system is stable and the equilibrium point is exponentially attractive. This extended notion of exponential stability is required since the feedback, and hence the closed-loop system, is not Lipschitz. However, it is shown that the convergence rate of a Lipschitz closed-loop driftless system cannot be bounded by an exponential envelope. The synthesis methods generate feedbacks which are smooth on ℝ^n \ {0}. The solutions of the closed-loop system are proven to be unique in this case. In addition, the control inputs for many driftless systems are velocities. For this class of systems it is more appropriate for the control law to specify actuator forces instead of velocities. We have extended the kinematic velocity controllers to controllers which command forces and still p-exponentially stabilize the system. Perhaps the ultimate justification of the methods proposed in this thesis are the experimental results. The experiments demonstrate the superior convergence performance of the p-exponential stabilizers versus traditional smooth feedbacks. The experiments also highlight the importance of transformation conditioning in the feedbacks. Other design issues, such as scaling the measured states to eliminate hunting, are discussed. The methods in this thesis bring the practical control of strongly nonlinear systems one step closer

6th International congress of the Serbian society of mechanics: Review

Ovaj rad prikazuje najvažnije informacije o 6. kongresu Srpskog društva za mehaniku, koji je održan na Tari od 19. do 21. juna 2017. Kongres je organizovan od strane Srpskog društva za mehaniku. Dat je kratak prikaz najznačajnijih radova predstavljenih na ovom kongresu, a koji se bave teorijskom i primenjenom mehanikom.This paper presents the most important information and describes the activities of the 6th Congress of the Serbian Society of Mechanics which was held on mountain Tara, on 19- 21 June, 2017. The Congress was organized by the Serbian Society of Mechanics. Brief summaries of the plenary lectures and some of 99 accepted papers, which admittedly attracted the most interest were shown as well

Planning Framework for Robotic Pizza Dough Stretching with a Rolling Pin

Stretching a pizza dough with a rolling pin is a nonprehensile manipulation. Since the object is deformable, force closure cannot be established, and the manipulation is carried out in a nonprehensile way. The framework of this pizza dough stretching application that is explained in this chapter consists of four sub-procedures: (i) recognition of the pizza dough on a plate, (ii) planning the necessary steps to shape the pizza dough to the desired form, (iii) path generation for a rolling pin to execute the output of the pizza dough planner, and (iv) inverse kinematics for the bi-manual robot to grasp and control the rolling pin properly. Using the deformable object model described in Chap. 3, each sub-procedure of the proposed framework is explained sequentially