State-space representation In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. "State space" refers to the space whose axes are the state variables. The state of the system can be represented as a vector within that space. To abstract from the number of inputs, outputs and states, these variables are expressed as vectors. inputs and outputs, we would otherwise have to write down Laplace transforms to encode all the information about a system. State variables The internal state variables are the smallest possible subset of system variables that can represent the entire state of the system at any given time. The minimum number of state variables required to represent a given system, , is usually equal to the order of the system's defining differential equation. Linear systems Block diagram representation of the linear state-space equations inputs, outputs and where: ). .
Inverted pendulum Balancing cart, a simple robotics system 1976. A second type of inverted pendulum is a tiltmeter for tall structures, which consists of a wire anchored to the bottom of the foundation and attached to a float in a pool of oil at the top of the structure that has devices for measuring movement of the neutral position of the float away from its original position. Overview Another way that an inverted pendulum may be stabilized, without any feedback or control mechanism, is by oscillating the support rapidly up and down. Equations of motion The equations of motion of inverted pendulums are dependent on what constraints are placed on the motion of the pendulum. Stationary pivot point Where is the angular acceleration of the pendulum, is the standard gravity on the surface of the Earth, is the length of the pendulum, and is the angular displacement measured from the equilibrium position. When added to both sides, it will have the same sign as the angular acceleration term: Mass and 1.
Anatta In Buddhism, the term anattā (Pāli) or anātman (Sanskrit: अनात्मन्) refers to the perception of "not-self", recommended as one of the seven beneficial perceptions, which along with the perception of dukkha, and anicca, is also formally classified among the three marks of existence. Anatta in the Nikayas The ancient Indian word for self or essence is attā (Pāli) or ātman (Sanskrit), and is often thought to be an eternal substance that persists despite death. Hence the term anatta is often interpreted as referring to the denial of a self or essence. Taken together with the perceptions of anicca (impermanence) and dukkha (imperfection), anatta (not self) perception is the last of the three marks of existence, which when grasped strategically, leads to dispassion (nibbida). Karma and Anatta Skillful action Because most philosophers focus on asserting or rejecting a self, when people approach Buddhism, they assume it is answering the same questions. Views on self
Dynamical system The Lorenz attractor arises in the study of the Lorenz Oscillator, a dynamical system. Overview Before the advent of computers, finding an orbit required sophisticated mathematical techniques and could be accomplished only for a small class of dynamical systems. Numerical methods implemented on electronic computing machines have simplified the task of determining the orbits of a dynamical system. For simple dynamical systems, knowing the trajectory is often sufficient, but most dynamical systems are too complicated to be understood in terms of individual trajectories. The systems studied may only be known approximately—the parameters of the system may not be known precisely or terms may be missing from the equations. History Many people regard Henri Poincaré as the founder of dynamical systems. Poincaré published two now classical monographs, "New Methods of Celestial Mechanics" (1892–1899) and "Lectures on Celestial Mechanics" (1905–1910). Basic definitions Flows
Piezoelectric motor Insides of a slip-stick piezoelectric motor. Two piezoelectric crystals are visible that provide the mechanical torque. A piezoelectric motor or piezo motor is a type of electric motor based upon the change in shape of a piezoelectric material when an electric field is applied. Current designs A slip-stick actuator. Motors are made in both linear and rotary types. Of these, one drive technique is to use piezoelectric ceramics to push a stator. A second drive technique is illustrated by the Squiggle motor, in which piezoelectric elements are bonded orthogonally to a nut and their ultrasonic vibrations rotate and translate a central lead screw. Locking mechanisms The non-power behaviour of the second type of motor is locked, as the drive screw is locked by the threads on the nut. Stepping actions Piezoelectric motor Fig. 1: Stepping stages of Normally Free motor Then the locking group triggered in stage one is released (in Normally Locking motors, the other is triggered).
Bundle theory According to bundle theory, an object consists of its properties and nothing more: thus neither can there be an object without properties nor can one even conceive of such an object; for example, bundle theory claims that thinking of an apple compels one also to think of its color, its shape, the fact that it is a kind of fruit, its cells, its taste, or at least one other of its properties. Thus, the theory asserts that the apple is no more than the collection of its properties. In particular, there is no substance in which the properties inhere. Arguments for the bundle theory The difficulty in conceiving of or describing an object without also conceiving of or describing its properties is a common justification for bundle theory, especially among current philosophers in the Anglo-American tradition. Whether a relation of an object is one of its properties may complicate such an argument. Objections to the bundle theory Compresence objection See also References
Calculus History Modern calculus was developed in 17th century Europe by Isaac Newton and Gottfried Wilhelm Leibniz (see the Leibniz–Newton calculus controversy), but elements of it have appeared in ancient Greece, China, medieval Europe, India, and the Middle East. Ancient The ancient period introduced some of the ideas that led to integral calculus, but does not seem to have developed these ideas in a rigorous and systematic way. Medieval Modern In Europe, the foundational work was a treatise due to Bonaventura Cavalieri, who argued that volumes and areas should be computed as the sums of the volumes and areas of infinitesimally thin cross-sections. These ideas were arranged into a true calculus of infinitesimals by Gottfried Wilhelm Leibniz, who was originally accused of plagiarism by Newton. He is now regarded as an independent inventor of and contributor to calculus. Leibniz and Newton are usually both credited with the invention of calculus. Foundations
Gyroscope A gyroscope Gyroscopes based on other operating principles also exist, such as the electronic, microchip-packaged MEMS gyroscope devices found in consumer electronic devices, solid-state ring lasers, fibre optic gyroscopes, and the extremely sensitive quantum gyroscope. Applications of gyroscopes include inertial navigation systems where magnetic compasses would not work (as in the Hubble telescope) or would not be precise enough (as in ICBMs), or for the stabilization of flying vehicles like radio-controlled helicopters or unmanned aerial vehicles. Due to their precision, gyroscopes are also used in gyrotheodolites to maintain direction in tunnel mining. Description and diagram Diagram of a gyro wheel. The outer gimbal or ring, which is the gyroscope frame, is mounted so as to pivot about an axis in its own plane determined by the support. The axle of the spinning wheel defines the spin axis. Animation of a gyro wheel in action History Properties Variations
Object (philosophy) The pragmatist Charles S. Peirce defines the broad notion of an object as anything that we can think or talk about. In a general sense it is any entity: the pyramids, Alpha Centauri, the number seven, a disbelief in predestination or the fear of cats. In a strict sense it refers to any definite being. A related notion is objecthood. Objecthood is the state of being an object. The notion of an object must address two problems: the change problem and the problem of substance. An attribute of an object is called a property if it can be experienced (e.g. its color, size, weight, smell, taste, and location). Because substances are only experienced through their properties a substance itself is never directly experienced. Some philosophies[which?] In the Mūlamadhyamakakārikā Nagarjuna seizes the dichotomy between objects as collections of properties or as separate from those properties to demonstrate that both assertions fall apart under analysis. Russell, Bertrand (1948).
Conceptual model A conceptual model is a model made of the composition of concepts, which are used to help people know, understand, or simulate a subject the model represents. Some models are physical objects; for example, a toy model which may be assembled, and may be made to work like the object it represents. The term conceptual model may be used to refer to models which are formed after a conceptualization (generalization) process in the mind. Conceptual models represent human intentions or semantics[dubious ]. Conceptualization from observation of physical existence and conceptual modeling are the necessary means that humans employ to think and solve problems. Models of concepts and models that are conceptual The term conceptual model is ambiguous. Type and scope of conceptual models Overview A conceptual model's primary objective is to convey the fundamental principles and basic functionality of the system in which it represents. Techniques
Shadow Hand The Shadow C6M Smart Motor Hand in front of the Shadow C3 Dexterous Air Muscle Hand Comparison of The Shadow Dexterous Hand with the human hand. The Shadow Dexterous Robot Hand is the first commercially available robot hand from the company, and follows a series of prototype humanoid hand and arm systems. Design The Shadow Dexterous Hand has been designed to be as similar as possible to the average hand of the human male. The Shadow Dexterous Hand has 24 joints. The hand is available in both electric motor driven and pneumatic muscle driven models. All hands have Hall effect sensors integrated into every joint to provide precise positional feedback. The Shadow Hand software system is based on Robot Operating System, through which configuration, calibration, simulation and control of the hand is implemented. See also Robonaut Further reading References External links