Kinematics: Describing the Motions of Spacecraft

Start Date: 09/04/2018

Course Type: Common Course

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About Course

The movement of bodies in space (like spacecraft, satellites, and space stations) must be predicted and controlled with precision in order to ensure safety and efficacy. Kinematics is a field that develops descriptions and predictions of the motion of these bodies in 3D space. This course in Kinematics covers four major topic areas: an introduction to particle kinematics, a deep dive into rigid body kinematics in two parts (starting with classic descriptions of motion using the directional cosine matrix and Euler angles, and concluding with a review of modern descriptors like quaternions and Classical and Modified Rodrigues parameters). The course ends with a look at static attitude determination, using modern algorithms to predict and execute relative orientations of bodies in space. After this course, you will be able to... * Differentiate a vector as seen by another rotating frame and derive frame dependent velocity and acceleration vectors * Apply the Transport Theorem to solve kinematic particle problems and translate between various sets of attitude descriptions * Add and subtract relative attitude descriptions and integrate those descriptions numerically to predict orientations over time * Derive the fundamental attitude coordinate properties of rigid bodies and determine attitude from a series of heading measurements

Course Syllabus

This module provides an overview of orientation descriptions of rigid bodies. The 3D heading is here described using either the direction cosine matrix (DCM) or the Euler angle sets. For each set the fundamental attitude addition and subtracts are discussed, as well as the differential kinematic equation which relates coordinate rates to the body angular velocity vector.

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Course Introduction

The movement of bodies in space (like spacecraft, satellites, and space stations) must be predicted

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Article Example
Kinematics Rotational or angular kinematics is the description of the rotation of an object. The description of rotation requires some method for describing orientation. Common descriptions include Euler angles and the kinematics of turns induced by algebraic products.
Stellar kinematics In astronomy, stellar kinematics is the observational study or measurement of the kinematics or motions of stars through space. The subject of stellar kinematics encompasses the measurement of stellar velocities in the Milky Way and its satellites as well as the measurement of the internal kinematics of more distant galaxies. Measurement of the kinematics of stars in different subcomponents of the Milky Way including the thin disk, the thick disk, the bulge, and the stellar halo provides important information about the formation and evolutionary history of our Galaxy. Kinematic measurements can also identify exotic phenomena such as hypervelocity stars escaping from the Milky Way, which are interpreted as the result of gravitational encounters of binary stars with the supermassive black hole at the Galactic Center.
Kinematics The equations of translational kinematics can easily be extended to planar rotational kinematics for constant angular acceleration with simple variable exchanges:
Kinematics Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies. In mechanical engineering, robotics, and biomechanics kinematics is used to describe the motion of systems composed of joined parts (multi-link systems) such as an engine, a robotic arm or the human skeleton.
Kinematics equations These equations are the kinematics equations of the parallel chain.
Robot kinematics A fundamental tool in robot kinematics is the kinematics equations of the kinematic chains that form the robot. These non-linear equations are used to map the joint parameters to the configuration of the robot system. Kinematics equations are also used in biomechanics of the skeleton and computer animation of articulated characters.
Forward kinematics The kinematics equations of the robot are used in robotics, computer games, and animation. The reverse process that computes the joint parameters that achieve a specified position of the end-effector is known as inverse kinematics.
Inverse kinematics In robotics, inverse kinematics makes use of the kinematics equations to determine the joint parameters that provide a desired position for each of the robot's end-effectors. Specification of the movement of a robot so that its end-effectors achieve the desired tasks is known as motion planning. Inverse kinematics transforms the motion plan into joint actuator trajectories for the robot. Similar formulae determine the positions of the skeleton of an animated character that is to move in a particular way in a film, or of a vehicle such as a car or boat containing the camera which is shooting a scene of a film. Once a vehicle's motions are known, they can be used to determine the constantly-changing viewpoint for computer-generated imagery of objects in the landscape such as buildings, so that these objects change in perspective while not themselves appearing to move as the vehicle-borne camera goes past them.
Kinematics equations From this point of view the kinematics equations can be used in two different ways. The first called "forward kinematics" uses specified values for the joint parameters to compute the end-effector position and orientation. The second called "inverse kinematics" uses the position and orientation of the end-effector to compute the joint parameters values.
Kinematics Kinematics is the branch of classical mechanics which describes the motion of points (alternatively "particles"), bodies (objects), and systems of bodies without consideration of the masses of those objects nor the forces that may have caused the motion. Kinematics as a field of study is often referred to as the "geometry of motion" and as such may be seen as a branch of mathematics. Kinematics begins with a description of the geometry of the system and the initial conditions of known values of the position, velocity and or acceleration of various points that are a part of the system, then from geometrical arguments it can determine the position, the velocity and the acceleration of any part of the system. The study of the influence of forces acting on masses falls within the purview of kinetics. For further details, see analytical dynamics.
Kinematics equations Remarkably, while the forward kinematics of a serial chain is a direct calculation of a single matrix equation, the forward kinematics of a parallel chain requires the simultaneous solution of multiple matrix equations which presents a significant challenge.
Inverse kinematics The movement of a kinematic chain, whether it is a robot or an animated character is modeled by the kinematics equations of the chain. These equations define the configuration of the chain in terms of its joint parameters. Forward kinematics uses the joint parameters to compute the configuration of the chain, and inverse kinematics reverses this calculation to determine the joint parameters that achieves a desired configuration.
Robot kinematics Forward kinematics uses the kinematic equations of a robot to compute the position of the end-effector from specified values for the joint parameters. The reverse process that computes the joint parameters that achieve a specified position of the end-effector is known as inverse kinematics. The dimensions of the robot and its kinematics equations define the volume of space reachable by the robot, known as its workspace.
Robot kinematics Forward kinematics specifies the joint parameters and computes the configuration of the chain. For serial manipulators this is achieved by direct substitution of the joint parameters into the forward kinematics equations for the serial chain. For parallel manipulators substitution of the joint parameters into the kinematics equations requires solution of the a set of polynomial constraints to determine the set of possible end-effector locations. In case of a Stewart platform there are 40 configurations associated with a specific set of joint parameters.
Stellar kinematics Stellar kinematics is related to but distinct from the subject of stellar dynamics, which involves the theoretical study or modeling of the motions of stars under the influence of gravity. Stellar-dynamical models of systems such as galaxies or star clusters are often compared with or tested against stellar-kinematic data to study their evolutionary history and mass distributions, and to detect the presence of dark matter or supermassive black holes through their gravitational influence on stellar orbits.
Inverse kinematics An animated figure is modeled with a skeleton of rigid segments connected with joints, called a kinematic chain. The kinematics equations of the figure define the relationship between the joint angles of the figure and its pose or configuration. The forward kinematic animation problem uses the kinematics equations to determine the pose given the joint angles. The "inverse kinematics problem" computes the joint angles for a desired pose of the figure.
Inverse kinematics There are many methods of modelling and solving inverse kinematics problems. The most flexible of these methods typically rely on iterative optimization to seek out an approximate solution, due to the difficulty of inverting the forward kinematics equation and the possibility of an empty solution space. The core idea behind several of these methods is to model the forward kinematics equation using a Taylor series expansion, which can be simpler to invert and solve than the original system.
Kinematics equations These equations are called the kinematics equations of the serial chain.
Robot kinematics Inverse kinematics specifies the end-effector location and computes the associated joint angles. For serial manipulators this requires solution of a set of polynomials obtained from the kinematics equations and yields multiple configurations for the chain. The case of a general 6R serial manipulator (a serial chain with six revolute joints) yields sixteen different inverse kinematics solutions, which are solutions of a sixteenth degree polynomial. For parallel manipulators, the specification of the end-effector location simplifies the kinematics equations, which yields formulas for the joint parameters.
Inverse kinematics While analytical solutions to the inverse kinematics problem exist for a wide range of kinematic chains, computer modeling and animation tools often use Newton's method to solve the non-linear kinematics equations.