All Notes
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Algorithms are sets of steps for computer programs to accomplish tasks. They include methods like binary search, sorting, and recursive techniques.
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Asymptotic notation measures algorithm efficiency. It includes notations like Big-Theta, Big-O, and Big-Omega.
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Binary search is an algorithm for finding an item in a sorted list. It works by repeatedly dividing the list in half until the item is found.
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Divide and conquer algorithms solve problems by breaking them into smaller sub-problems. This approach is used in merge sort and other efficient algorithms.
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Insertion sort arranges elements by comparing and inserting each into a sorted portion. It runs in O(n^2) time, with a best-case time of Θ(n).
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Recursive algorithms solve problems by breaking them down into smaller instances of the same problem.
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Selection sort is a simple algorithm that sorts an array by repeatedly selecting the next-smallest element and swapping it into place. It has a running time of Θ(n^2) in all cases.
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Ciphers are mechanical operations that transform individual symbols according to an algorithm. They operate on syntax, unlike codes, which operate on semantics and meaning.
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Cryptography involves using ciphers to securely communicate messages. It is a key field in modern world communication.
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Cryptography involves techniques like the Caesar cipher and one-time pad to secure messages. These methods use shifting and random sequences to encrypt data.
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Modern cryptography relies on mathematical concepts like the fundamental theorem of arithmetic. It uses one-sided functions, such as modular arithmetic, to secure data.
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Modular arithmetic involves operations on integers where only the remainder is considered. It has properties and applications in cryptography and computer science.
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A primality test determines if a number is prime or composite. It checks divisibility from 1 to the square root of the number.
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Dynamic programming is a collection of algorithms that compute optimal policies given a perfect model of the environment. It uses the value function to search for better policies.
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Finite Markov decision processes involve an agent and environment interacting at discrete time steps. The agent receives a state representation and selects actions to maximize a reward signal.
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Reinforcement learning involves learning to maximize a numerical reward signal. It is a class of solution methods for problems where an agents actions influence its inputs.
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Monte Carlo methods solve reinforcement learning problems by averaging sample returns. They require only experience from environment interactions.
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The multi-arm bandit problem involves choosing among multiple options to maximize expected total reward. It requires balancing exploration and exploitation to achieve optimal results.
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Reinforcement learning involves maximizing a numerical reward signal. It is a field that studies problems and solution methods for learning optimal actions.
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Steganography hides information in plain sight by making it invisible. It differs from cryptography, which encrypts information using secret codes.
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Adaptive control involves systems with time-varying parameters. It includes indirect and direct methods to address system model uncertainties.
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Adaptive control addresses incomplete or imprecise system models. It aims to achieve stability, robustness, and tracking despite uncertainties.
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This paper introduces a novel control approach for discrete-time nonlinear systems. It proposes an equivalent PFDL description and estimates parameter Φ online.
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Data-driven model-free adaptive control is applied to MIMO nonlinear discrete-time systems. A general system is considered with input and output of the same length.
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Data-driven control methods are categorized into three main categories. They include online data-based, offline data-based, and iterative data-based methods, such as SPSA, MFAC, and UC.
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MFAC is a data-driven approach to adaptive control. It uses pseudo-partial derivatives to build a dynamic linearization model from input/output measurement data.
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Model-free adaptive control is used to predict and control nonlinear systems. It adapts to aperiodic jamming attacks by modifying system estimation and control laws.
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MRAC refers to Model Reference Adaptive Control. It is a control method that adjusts parameters.
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Data-driven control uses input/output data to tune controller parameters. It designs controllers without explicit mathematical models of the controlled process.
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The Lambert W function is used to study linear time-delayed systems. It helps analyze systems with infinitely many eigenvalues.
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Linear time-delayed systems have infinitely many eigenvalues. Their stability depends on parameters $A$, $A_d$, and $ au$.
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Overview of all the notes and projects
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current robotic projects.
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2DoF robot control involves regulating a robots movement with two degrees of freedom. This is relevant to the Single Leg Project in robotics.
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Impedance control regulates a robots dynamic behavior at interaction ports with its environment.
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The Linear Complementarity Problem (LCP) seeks vectors that satisfy specific constraints. It involves a matrix and vector to find non-negative vectors satisfying a complementarity condition.
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The mathematical model of a single leg robot can be written using the Newtonian or Lagrangian method. The Lagrangian method, which is explained in this page, derives equations of motion by defining kinetic and potential energies.
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Robot leg motion is governed by equations such as Newtons and Eulers. These equations simplify during flight and stance phases.
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Single leg control is a fundamental aspect of legged robotics. Controlling a single leg with multiple degrees of freedom is a key step in developing more complex legged robots.
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Single leg robots use Permanent Magnet Synchronous Motors (PMSMs). PMSMs control torque through a rotating magnetic field.
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The Single Leg Robot Controller utilizes Go-M8010-6 motors. Basic tests are being conducted on the motor, with full SLIP tests planned.
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A numerical model for a single leg robot was developed using Lagrangian dynamics. The model simulates the legs motion, switching between different modes based on contact with the ground.
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Single leg robot simulations were conducted using various tools, including MATLAB and Pybullet. These simulations tested the robots dynamics and control systems.
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System identification is applied to a single leg robot. This process involves modeling and analyzing its dynamics.
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Stability of legged robots is analyzed through concepts like fixed points and limit cycles. These concepts relate to the robots ability to maintain safe postures and motions.
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Kinematics studies the relationship between joint and end effector motion. It is used to derive equations describing robot movement.
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