Read to Respond: Labor

R2R final logoOur “Read to Respond” series addresses the current climate of misinformation by highlighting articles and books that encourage thoughtful, educated debate on today’s most pressing issues. This post focuses on labor, worker’s rights, and neoliberalism. Read, reflect, and share these resources in and out of the classroom to keep these important conversations going.

Labor

These articles are freely available until December 15, 2017. Follow along with the series over the next several months and share your thoughts with #ReadtoRespond.

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  1. sure these appear say prof dr mircea orasanu Abstract:

    The present paper investigates why Logical Empiricists remained silent about one of the most philosophy-laden matters of theoretical physics of the day, the Principle of Least Action (PLA). In the two decades around 1900, the PLA enjoyed a remarkable renaissance as a formal unification of mechanics, electrodynamics, thermodynamics, and relativity theory. Taking Ernst Mach’s historico-critical stance, it could be liberated from much of its physico-theological dross. Variational calculus, the mathematical discipline on which the PLA was based, obtained a new rigorous basis. These three developments prompted Max Planck to consider the PLA as formal embodiment of his convergent realist methodology. Typically rejecting ontological reductionism, David Hilbert took the PLA as the key concept in his axiomatizations of physical theories. It served one of the main goals of the axiomatic method: ‘deepening the foundations’. Although Moritz Schlick was a student of Planck’s, and Hans Hahn and Philipp Frank enjoyed close ties to Göttingen, the PLA became a veritable Shibboleth to them. Rather than being worried by its historical connections with teleology and determinism, they erroneously identified Hilbert’s axiomatic method tout court with Planck’s metaphysical realism. Logical Empiricists’ strict containment policy against metaphysics required so strict a separation between physics and mathematics to exclude even those features of the PLA and the axiomatic method not tainted with metaphysics.

    Keywords:
    Principle of Least Action, calculus of variations, Hilbert’s axiomatic method in physics, Mach-Planck controversy, Logical Empiricism, Moritz Schlick, Hans Hahn, Philipp Frank.

    Over the centuries, no other principle of classical physics has to a larger extent nourished exalted hopes into a universal theory, has constantly been plagued by mathematical counterexamples, and has ignited metaphysical controversies about causality and teleology than did the Principle of Least Action (henceforth PLA). After some decades of relative neglect, by the end of the 19th century the PLA and its kin enjoyed a remarkable renaissance on three levels.
    Since the work of Hermann von Helmholtz, the PLA had become a very successful scheme applicable not only in mechanics, but also in electrodynamics, thermodynamics and relativity theory. Did this spectacular success indicate that physicists possessed – to cite Helmholtz – “a valuable heuristic principle and leitmotif in striving for a formulation of the laws of new classes of phenomena” (Helmholtz, 1886, p. 210), or were these principles – as Ernst Mach held – just useful rules that served the economy of thought in various domains of experience?
    A second important reorientation took place in variational calculus, the mathematical discipline on which the PLA was based and which had accompanied it through more than two centuries of philosophical debates. Karl Weierstraß’ critical investigations demonstrated that the precise relationship between the PLA and the differential equations resulting from it was extremely subtle, and that physicists’ customary reasoning in solving important cases only obtained under supplementary conditions. The generations of Euler and Lagrange typically had identified the PLA and the differential equations resulting from it regardless of their metaphysical attitude towards the PLA and the quantity of action. In the 19th century, variational calculus was regarded as a very useful method in analysis the application of which ho

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  2. also here we consider some as say prof dr mircea orasanu and prof horia orasanu as followings
    LAGRANGIAN AND CONSTRAINT OPTIMIZATION
    Author Horia Orasanu
    ABSTRACT
    Locomotion of a snake-like structure in accordance with the serpenoid curve, i.e. lateral undulation, is achieved if the joints of the robot move according to the reference joint trajectories in the form of a sinusoidal function with specified amplitude, frequency, and phase shift. In particular, using the foregoing defined new states, we define a constraint function for the ith joint of the snake robot by
    1 INTRODUCTION
    A fundamental work in the area of snake robots was presented by Hirose [5]. In this work, Hirose considers empirical studies of biological snakes to derive a mathematical approximation of the most common gait pattern among biological snakes, known as lateral undulation. In particular, the shape of a snake conducting lateral undulation can be described by a planar curve (the serpenoid curve) with coordinates in the x-y plane along the curve at arc length s given by
    x(s)=∫0scos(acos(bz)+cz)dz
    (43)
    y(s)=∫0ssin(acos(bz)+cz)dz
    (44)
    where a, b, and c are positive scalars.
    Φi = αsin(η + (i − 1)δ) + ϕo
    (45)
    where i∈{1,…,N−1}, α denotes the amplitude of the sinusoidal joint motion, and δ is a phase shift that is used to keep the joints out of phase. Moreover, ϕo is an offset value that is identical for all of the joints. It was illustrated in [16] how the offset value ϕo affects the orientation of the snake robot in the plane. Building further on this insight, we consider the second-order time derivative of ϕo in the form of a dynamic compensator, which will be used to control the orientation of the robot. In particular, through this control term, we modify the orientation of the robot in accordance with a reference orientation. This will be done by adding an offset angle to the reference trajectory of each joint. To define the guidance law, without loss of generality, we assign the global coordinate system such that the global x-axis is aligned with the desired path. Consequently, the position of the CM of the robot along the y-axis, denoted by py, defines the shortest distance between the robot and the desired path, often referred to as the cross-track error. In order to solve the path following problem, we use the LOS guidance law as a virtual holonomic constraint, which defines the desired head angle as a function of the cross-track error as
    ΦN=−tan−1(pyΔ)
    In particular, we use a line-of-sight (LOS) guidance law as the reference angle for the head link. LOS guidance is a much-used method in marine control systems (see, e.g. [27]). In general, guidance-based control strategies are based on defining a reference heading angle for the vehicle through a guidance law and designing a controller to track this angle [27].

    If the basis physics is postulated but not known, a computer simulation can relate the theory to observations on complex systems and thus test the theory.
    A wide range of numerical techniques are available, from simple searches to sophisticated methods, such as annealing, an algorithm for finding global minima which was inspired by an actual physical process. Some of the techniques are repetitive applications of deterministic equations. Others invoke stochastic processes (using “random” numbers), to focus on the important features.
    While most applications of such simulations yield expected results, surprises do occur. This is analogous to an unexpected result from an experiment. Either the simulation/experiment went wrong (usual) or a new aspect of nature has been uncovered (rare). Examples of the latter are the identification of constants of motion in chaotic systems and the discovery of runaway motion in the drift and diffusion of ions in gas. Such discoveries are followed by “proper” theories and “proper” experiments, but the computer plays a vital role in the research.
    The research of Professor Gatland involves data analysis and the mathematical modeling and simulation of microscopic physical processes. These activities encompass both research and instruction.
    In this lecture we recall the definitions of autonomous and non autonomous Dynamical Systems as well as their different concepts of attractors. After that we introduce the different notions of robustness of attractors under perturbation (Upper semicontinuity, Lower semicontinuity, Topological structural stability and Structural stability) and give conditions on the dynamical systems so that robustness is attained. We show that enforcing the appropriately defined virtual holonomic constraints for the configuration variables implies that the robot converges to and follows a desired geometric path. Numerical simulations and experimental rMethods
    In this section, we derive the kinematic model along with the dynamic equations of motion of the snake robot in a Lagrangian framework. Moreover, we use partial feedback linearization to write the model in a simpler form for model-based control design.
    In order to perform control design, we need to write the governing equations of the system in an implementable way. This is often done by choosing a local coordinate chart and writing the system equations with respect to (w.r.t.) these coordinates. According to the illustration of the snake robot in Figure Figure1,1, we choose the vector of the generalized coordinates of the N-link snake robot as x = [q1,q2,…,qN−1,θN,px,py]T ∈ ℝN+2, where qi with i∈{1,…,N−1} denotes the ith joint angle, θN denotes the head angle, and the pair (px,py) describes the position of the CM of the robot w.r.t. the global x−y axes. Since the robot is not subject to nonholonomic velocity constraints, the vector of the generalized velocities is defined as x˙=[q˙1,q˙2,…,q˙N−1,θ˙N,p˙x,p˙y]T∈RN+2. Using these coordinates, it is possible to specify the kinematic map of the robot. In this paper, we denote the first N elements of the vector x, i.e. (q1,…,qN−1,θN), as the angular coordinates, and the corresponding dynamics as the angular dynamics of the system.

    Figure 1
    An illustration of the N -link snake robot. Kinematic parameters of the snake robot.

    This is due to the fact that it is usually not straightforward to integrate the anisotropic external dissipative forces, i.e. ground friction forces, acting on these complex robotic structures into their Euler-Lagrange equations of motion. However, ground friction forces have been proved to play a fundamental role in snake robot locomotion (see, e.g. [16]). In this paper, we derive the equations of motion of the snake robot in a Lagrangian framework, i.e. treating the robot as a whole and performing the analysis using a Lagrangian function, which is simple to follow and better suited for studying advanced mechanical phenomena such as elastic link deformations [25], which might be insightful for future research challenges on snake robots. Moreover, we integrate the anisotropic friction forces into these equations using the Jacobian matrices of the links, which gives a straightforward mapping of these forces for the equations of motion.
    Snake robots are a class of simple mechanical systems, where the Lagrangian L(qa,x˙) is defined as the difference between the kinetic energy K(qa,x˙) and potential energy 𝒫(x) of the system [26]. Since the planar snake robot is not subject to any potential field, i.e. −∇𝒫(x) = 0, we may write the Lagrangian equal to the kinetic energy, which is the sum of the translational and the rotational kinetic energy of the robot:
    L(qa,x˙)=K(qa,x˙)=12m∑i=1N(p˙2x,i+p˙2y,i)+12J∑i=1Nθ˙2i
    (9)
    where m and J denote the uniformly distributed mass and moment of inertia of the links, respectively. Using the Lagrangian function (9), we write the Euler-Lagrange equations of motion of the controlled system as
    ddt[∂L(qa,x˙)∂x˙i]−∂L(qa,x˙)∂xi=(B(x)τ−τf)i
    (10)
    where i∈{1,…,N+2}, B(x) = [ej] ∈ ℝ(N+2)×(N−1) is the full column rank actuator configuration matrix, where ej denotes the jth standard basis vector in ℝN+2. Moreover, B(x)τ ∈ ℝN+2 with τ = [τ1,…,τN−1]T ∈ ℝN−1 stands for the generalized forces resulting from the control inputs. Furthermore, τf=[τ1f,…,τN+2f]T∈RN+2 denotes viscous and Coulomb friction forces acting on (N+2) DOF of the system. The controlled Euler-Lagrange equations (10) can also be written in the form of a second-order differential equation as
    M(qa)x¨+C(x,x˙)x˙=B(x)τ−τf
    (11)
    where M(qa) ∈ ℝ(N+2)×(N+2) is the positive definite symmetric inertia matrix, C(x,x˙)x˙∈RN+2 denotes the generalized Coriolis and centripetal forces, and the right-hand side terms denote the external forces acting on the system. The fact that the inertia matrix is only a function of the directly actuated shape variables qa is a direct consequence of the invariance of the Lagrangian
    The geometry of the problem
    The (N+2)-dimensional configuration space of the snake robot is denoted as 𝒬 = 𝒮 × 𝒢, which is composed of the shape space and a Lie group which is freely and properly acting on the configuration space. In particular, the shape variables, i.e. qa=(q1,…,qN−1), which define the internal configuration of the robot and which we have direct control on, take values in . Moreover, the position variables, i.e. qu=(θN,px,py), which are passive DOF of the system, lie in . The velocity space of the robot is defined as the differentiable (2N+4)-dimensional tangent bundle of as T𝒬 = 𝕋N × ℝN+4, where 𝕋N denotes the N-torus in which the angular coordinates live. The free Lagrangian function of the robot ℒ:T𝒬 → ℝ is invariant under the given action of on . The coupling between the shape and the position variables causes the net displacement of the position variables, according to the cyclic motion of the shape variables, i.e. the gait pattern. Note that for simplicity of presentation, in this paper, we consider local representation of T𝒬 embedded in an (2N+4)-dimensional open subset of the Euclidean space ℝ2N+4. To this end, we separate the dynamic equations of the robot given by (11) into two subsets by taking x = [qa,qu]T ∈ ℝN+2, with qa ∈ ℝN−1 and qu ∈ ℝ3 which were defined in the subsection describing the geometry of the problem:
    m11(qa)q¨a+m12(qa)q¨u+h1(x,x˙)=ψ∈RN−1
    (20)
    m21(qa)q¨a+m22(qa)q¨u+h2(x,x˙)=03×1∈R3
    (21)
    where m11 ∈ ℝ(N−1)×(N−1), m12 ∈ ℝ(N−1)×3, m21 ∈ ℝ3×(N−1), and m22 ∈ ℝ3×3 denote the corresponding submatrices of the inertia matrix, and 03×1 = [0,0,0]T ∈ ℝ3. Furthermore, h1(x,x˙)∈RN−1 and h2(x,x˙)∈R3 include all the contributions of the Coriolis, centripetal, and friction forces. Moreover, ψ ∈ ℝN−1 denotes the non-zero part of the vector of control forces, i.e. B(x)τ = [ψ,03×1]T ∈ ℝN+2. From (21), we have
    q¨u=−m−122(h2+m21q¨a)∈R3
    (22)
    Substituting (22) into (20) yields
    (m11−m12m−122m21)q¨a−(m12m−122)h2+h1=ψ
    (23)
    For linearizing the dynamics of the directly actuated DOF, we apply the global transformation of the vector of control inputs as
    ψ=(m11−m12m−122m21)ϑ−(m12m−122)h2+h1
    (24)
    where 𝜗 = [𝜗1,𝜗2,…,𝜗N−1]T ∈ ℝN−1 is the vector of new control inputs. Consequently, the dynamic model (20)-(21) can be written in the following partially feedback linearized form
    q¨a=ϑ∈RN−1
    (25)
    q¨u=D(x,x˙)+C(qa)ϑ∈R3
    (26)
    with
    D(x,x˙)=−m−122(qa)h2(x,x˙)=[fθN,fx,fy]T∈R3
    (27)
    C(qa)==−m−122(qa)m21(qa)[βi(qa),0,0]T∈R3×(N−1)
    (28)
    where βi(qa):𝒬 → ℝ is a smooth scalar-valued function. It can be numerically shown that the value of βi is negative at any configuration qa ∈ 𝒬. Furthermore, fθN, fx, and fy denote the friction forces acting on θN, px, and py, respectively ( fθN also contains Coriolis forces besides the friction forces). For the aim of analysis and model-based control design, we write (25)-(26) in a more detailed form:
    q¨a=ϑ∈RN−1
    (29)
    θ¨N=fθN(x,x˙)+βi(qa)ϑi∈R
    (30)
    p¨x=fx(x,x˙)∈R
    (31)
    p¨y=fy(x,x˙)∈R
    (32)
    where the summation convention is applied in (30), and henceforth, to all the equations which contain repeated upper-lower indices (i.e. whenever an expression contains a repeated index, one as a subscript and the other as a superscript, summation is implied over this index [26]). The dynamical system (29)-(32) is in the form of a control-affine system with drift. In particular, the term
    A(x,x˙)=[q˙a,q˙u,0(N−1)×1,D(x,x˙)]T∈R2N+4
    (33)
    is called the drift vector field, which specifies the dynamics of the robot when the control input is zero. Furthermore, the columns of the matrix
    B(qa)=⎡⎣⎢⎢⎢⎢0(N+2)×(N−1)IN−1[β1(qa),…,βN−1(qa)]02×(N−1)⎤⎦⎥⎥⎥⎥∈R(2N+4)×(N−1)
    (34)
    are called the control vector fields, which enable us to control the internal configuration and consequently the orientation and the position of the robot in the plane.
    Remark2.
    The last two rows of the control vectors in (34) are composed of zero elements. This implies that the control forces have no direct effect on the dynamics of the position of the CM of the robot, i.e. (31)-(32). Furthermore, the dynamics of the position of the CM are coupled with the dynamics of the directly actuated shape variables qa, i.e. (29), only through the friction forces. Accordingly, in the absence of the friction forces, the linear momentum of the robot is a conserved quantity, and the position of the CM of the robot is not controllable.In this section, we state our control design objectives which will be followed throughout the remaining sections of the paper. In particular, we stress that for a complex mobile multi-link robotic structure such as a snake robot, formulating a pure path following, trajectory tracking, or maneuvering problem is unusual (for definitions of these problem formulations, see [27]). This is due to the fact that for a part of the state variables of the system (particularly the shape variables and the head angle), it is most natural to formulate the control problem as a trajectory tracking problem, while for the other state variables (particularly the position of the CM), we may formulate the problem as a path following or a maneuvering one.
    To formulate a combinational track-follow problem for the snake robot, which we define as a trajectory tracking formulation for a subset of the state variables, together with a path following formulation for the remaining subset, we introduce the error variable for the ith joint of the robot as
    yi = qi − Φi
    (35)
    where i∈{1,…,N−1}, and Φi ∈ ℝ denotes a function that defines the reference trajectory for the ith joint which will be chosen through the control design in the next section. The head angle error is defined as
    yN = θN − ΦN
    (36)
    where ΦN ∈ ℝ denotes the reference head angle for the robot.
    We divide the control objectives into three main parts. In the first part, the goal is to make the shape variables of the robot track given bounded smooth time-varying references, i.e. asymptotic trajectory tracking problem, such that
    limt→∞∥yi(t)∥=0
    (37)
    for all i∈{1,…,N−1}. Furthermore, we seek to control the head angle of the robot. The second part of the control objective is thus to make the head angle of the robot track a desired head angle such that
    limt→∞∥yN(t)∥=0
    (38)
    Moreover, we define a desired straight path that we want the CM of the snake robot to follow. This is defined as a smooth one-dimensional manifold 𝒫 ⊂ ℝ2, with coordinates in the x-y plane given by the pair (pxd,pyd), which are parameterized by a scalar time-dependent variable Θ(t) as
    𝒫 = {(pxd(Θ), pyd(Θ)) ∈ ℝ2:Θ ≥ 0}
    (39)
    We define the vector of the path following error variables for the position of the CM of the robot as p˜=[px(t)−pxd(Θ),py(t)−pyd(Θ)]T∈R2. Subsequently, the third part of the control objectives is defined as practical convergence (see, e.g. [4]) of the position of the CM of the robot to the desired path such that
    limt→∞sup∥p˜(t)∥≤ε
    (40)
    where ε ∈ ℝ>0 is an arbitrary positive scalar. Moreover, we require that Θ˙(t)≥0 and limt→∞Θ(t) = ∞ (forward motion along the path), and boundedness of the states of the controlled system.
    Go toVirtual holonomic constraints are specified through C1 coordinate-dependent functions Φi:𝒬 → ℝ which are called the constraint functions, in the relations of the form Φi(x)=0, which can be enforced through the feedback action. In particular, for the snake robot, we define a vector-valued function
    Φ = [Φ1,…,ΦN]T ∈ ℝN
    (41)
    in which every element defines one constraint function for the corresponding angular coordinate of the system.
    At this point, we augment the state vector of the system with three new states that in the following will be used in the control design. The introduction of these new variables to the state vector of the system, which will be used as constraint variables, is inspired by the notion of dynamic virtual holonomic constraints [21], i.e. virtual holonomic constraints which depend on the solutions of a dynamic compensator. The idea is to make the virtual holonomic constraints to depend on the variations of a dynamic parameter, which is used for controlling the system on the constraint manifold. The purpose of these additional states is explained below.
    1. We introduce two new states [ϕo,ϕ˙o]T∈R2 where the second-order time derivative of ϕo will be used as an additional control input that drives the snake robot towards the desired path by modifying the orientation of the robot in accordance with a path following guidance law.
    2. In the previous section, we defined the control objective for the joints and the head angle of the robot as a trajectory tracking problem. However, it is known that holonomic constraints are coordinate-dependent equality constraints of the form Φi(x)=0, where Φi is a time-independent function [25]. Thus, we remove this explicit time dependency from the reference joint trajectories by augmenting the state vector of the system with a new variable η, with η˙=2π/T and η(0)=0, where T denotes the period of the cyclic motion of the shape variables of the robot.
    Subsequently, we denote the augmented coordinate vector of the system by
    xˆ=[q1,…,qN−1,θN,px,py,ϕo,η]T∈RN+4
    (42)
    :

    References
    1. Liljebäck P, Stavdahl Ø, Beitnes A (2006) SnakeFighter – development of a water hydraulic fire fighting snake robot. In: Proc. IEEE international conference on control, automation, robotics, and vision ICARCV, Singapore.
    2. Wang Z, Appleton E (2003) The concept and research of a pipe crawling rescue robot. Adv Robot 17.4: 339–358.
    3. Fjerdingen SA, Liljebäck P, Transeth AA (2009) A snake-like robot for internal inspection of complex pipe structures (PIKo). In: Proc. IEEE/RSJ international conference on intelligent robots and systems, St. Louis, MO, USA.
    4. Dacic DB, Nesic D, Teel AR, Wang W. Path following for nonlinear systems with unstable zero dynamics: an averaging solution. IEEE Trans Automatic Control. 2011;56:880–886. doi: 10.1109/TAC.2011.2105130. [Cross Ref]
    5. Hirose S. Biologically inspired robots: snake-like locomotors and manipulators. Oxford, England: Oxford University Press; 1993.
    6. Matsuno F, Sato H (2005) Trajectory tracking control of snake robots based on dynamic model. In: Proc. IEEE international conference on robotics and automation, 3029–3034. 18-22 April 2005.
    7. Date H, Hoshi Y, Sampei M (2000) Locomotion control of a snake-like robot based on dynamic manipulability. In: Proc. IEEE/RSJ international conference on intelligent robots and systems, Takamatsu, Japan.
    8. Tanaka M, Matsuno F (2008) Control of 3-dimensional snake robots by using redundancy. In: Proc. IEEE international conference on robotics and automation, 1156–1161, Pasadena, CA.
    9. Ma S, Ohmameuda Y, Inoue K, Li B (2003) Control of a 3-dimensional snake-like robot. In: Proc. IEEE international conference on robotics and automation, vol. 2, 2067–2072, Taipei, Taiwan.
    10. Tanaka M, Matsuno F (2009) A study on sinus-lifting motion of a snake robot with switching constraints. In: Proc. IEEE international conference on robotics and automation, 2270–2275. 12-17 May 2009.
    11. Prautsch P, Mita T, Iwasaki T (2000) Analysis and control of a gait of snake robot. Trans IEE J Ind Appl Soc 120-D: 372–381.

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