|
Linear-quadratic Regulator Rapidly-exploring Random Tree
Linear-quadratic regulator rapidly exploring random tree (LQR-RRT) is a sampling based algorithm for kinodynamic planning. A solver is producing random actions which are forming a funnel in the state space. The generated tree is the action sequence which fulfills the cost function. The restriction is, that a prediction model, based on differential equations, is available to simulate a physical system. Motivation The control theory is using differential equations to describe complex physical systems like an inverted pendulum. A set of differential equations forms a physics engine which maps the control input to the state space of the system. The forward model is able to simulate the given domain. For example, if the user pushes a cart to the left, a pendulum mounted on the cart will react with a motion. The exact force is determined by newton's laws of motion. A solver, for example PID controllers and model predictive control, are able to bring the simulated system into a goal st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinodynamic Planning
In robotics and motion planning, kinodynamic planning is a class of problems for which velocity, acceleration, and force/torque bounds must be satisfied, together with kinematic constraints such as avoiding obstacles. The term was coined by Bruce Donald, Pat Xavier, John Canny, and John Reif. Donald et al. developed the first polynomial-time approximation schemes (PTAS) for the problem. By providing a provably polynomial-time ε-approximation algorithm, they resolved a long-standing open problem in optimal control. Their first paper considered time-optimal control ("fastest path") of a point mass under Newtonian dynamics, amidst polygonal (2D) or polyhedral (3D) obstacles, subject to state bounds on position, velocity, and acceleration. Later they extended the technique to many other cases, for example, to 3D open-chain kinematic robots under full Lagrangian dynamics In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-act ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any ''delay'', ''overshoot'', or ''steady-state error'' and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required. This controller monitors the controlled process variable (PV), and compares it with the reference or set point (SP). The difference between actual and desired value of the process variable, called the ''error'' signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects which are also studied are controllability and observability. Control theory is used in control sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton's Laws Of Motion
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force. # When a body is acted upon by a force, the time rate of change of its momentum equals the force. # If two bodies exert forces on each other, these forces have the same magnitude but opposite directions. The three laws of motion were first stated by Isaac Newton in his ''Philosophiæ Naturalis Principia Mathematica'' (''Mathematical Principles of Natural Philosophy''), originally published in 1687. Newton used them to investigate and explain the motion of many physical objects and systems, which laid the foundation for classical mechanics. In the time since Newton, the conceptual content of classical physics has been reformulated in alternative ways, involving differ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Predictive Control
Model predictive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models and in power electronics. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification. The main advantage of MPC is the fact that it allows the current timeslot to be optimized, while keeping future timeslots in account. This is achieved by optimizing a finite time-horizon, but only implementing the current timeslot and then optimizing again, repeatedly, thus differing from a linear–quadratic regulator ( LQR). Also MPC has the ability to anticipate future events and can take control actions accordingly. PID controllers do not have this predictive ability. MPC is nearly universally implemented as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State Space
A state space is the set of all possible configurations of a system. It is a useful abstraction for reasoning about the behavior of a given system and is widely used in the fields of artificial intelligence and game theory. For instance, the toy problem Vacuum World has a discrete finite state space in which there are a limited set of configurations that the vacuum and dirt can be in. A "counter" system, where states are the natural numbers starting at 1 and are incremented over time has an infinite discrete state space. The angular position of an undamped pendulum is a continuous (and therefore infinite) state space. Definition In the theory of dynamical systems, the state space of a discrete system defined by a function ''ƒ'' can be modeled as a directed graph where each possible state of the dynamical system is represented by a vertex with a directed edge from ''a'' to ''b'' if and only if ''ƒ''(''a'') = ''b''. This is known as a state diagram. For a co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Underactuation
Underactuation is a technical term used in robotics and control theory to describe mechanical systems that cannot be commanded to follow arbitrary trajectories in configuration space. This condition can occur for a number of reasons, the simplest of which is when the system has a lower number of actuators than degrees of freedom. In this case, the system is said to be ''trivially underactuated''. The class of underactuated mechanical systems is very rich and includes such diverse members as automobiles, airplanes, and even animals. Definition To understand the mathematical conditions which lead to underactuation, one must examine the dynamics that govern the systems in question. Newton's laws of motion dictate that the dynamics of mechanical systems are inherently second order. In general, these dynamics can be described by a second order differential equation: \ddot = f(q,\dot,u,t) Where: q \in \mathbb^n is the position state vector u \in \mathbb^m is the vector of co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MPC Scheme Basic
MPC, Mpc or mpc may refer to: Astronomy * Megaparsec (Mpc), unit of length used in astronomy * Minor Planet Center, Smithsonian Astrophysical Observatory ** ''Minor Planet Circulars'' (MPC, M.P.C. or MPCs), astronomical publication from the Minor Planet Center Businesses * Mai-Liao Power Corporation, Taiwan * Model Products Corporation, model kit manufacturer * Moving Picture Company, a visual effects company, London, UK * MPC, maker of encrypted mobile phones Computing and electronics * Media Player Classic, a software media player * MPC Computers, a former US computer maker * Multimedia PC * Multi Project Chip, sharing costs across projects * Musepack, an audio codec * Command-line client for the Music Player Daemon * Akai MPC, musicworkstations * Secure multi-party computation Economics * Marginal propensity to consume * Monetary Policy Committee (United Kingdom) Government and politics * Central African Patriotic Movement (MPC), a rebel group in the Central African R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trajectory (other)
A trajectory is the path a moving object follows through space. Types of trajectories include: * trajectory of a projectile ** lofted trajectory, a particular type of non-minimum energy ballistic trajectory * trajectory (fluid mechanics), the motion of a point in a moving fluid * in motion planning, the trajectory of a robotic motion * phase space trajectories of dynamical systems Trajectory may also refer to: * Trajectory (DC Comics), a DC Comics character ** Trajectory (The Flash episode), an episode of the U.S. TV series ''The Flash'' that includes the character ** Trajectory (Arrowverse), a fictional character appearing in the Arrowverse television franchise * trajectory hermeneutics, a liberal teaching of Christian Postmodernism * Trajectory Inc., an American ebook platform * trajectory optimization Trajectory optimization is the process of designing a trajectory that minimizes (or maximizes) some measure of performance while satisfying a set of constraints. Generally sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PID Controller
A proportional–integral–derivative controller (PID controller or three-term controller) is a control loop mechanism employing feedback that is widely used in industrial control systems and a variety of other applications requiring continuously modulated control. A PID controller continuously calculates an ''error value'' e(t) as the difference between a desired setpoint (SP) and a measured process variable (PV) and applies a correction based on proportional, integral, and derivative terms (denoted ''P'', ''I'', and ''D'' respectively), hence the name. In practical terms, PID automatically applies an accurate and responsive correction to a control function. An everyday example is the cruise control on a car, where ascending a hill would lower speed if constant engine power were applied. The controller's PID algorithm restores the measured speed to the desired speed with minimal delay and overshoot by increasing the power output of the engine in a controlled manner. The fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
