assign4_dynamics - SBE 2006 Dynamics Homework Problem...

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SBE 2006 Dynamics Homework Problem Preamble Imagine you are a test director at Johnson Space Center (JSC). You are interested in testing a training version of SAFER (Simplified Aid For EVA Rescue) to be used on the Precision Air Bearing Floor (PABF). The training version of the SAFER is designed to work only in one plane (i.e., the plane of motion parallel to the plane of the floor). The SAFER can be controlled in two ways: translation or rotation, depending on which jets are active at any time. Balanced jets in one direction will result in a force applied in the opposite direction. Counteracting jets on either side of the SAFER will result in a torque about the center of mass of the SAFER. The SAFER uses “bang-off-bang” control, meaning each jet is either fully on or fully off. A diagram of the training SAFER can be found below. In order to evaluate the performance of this SAFER model, you want to track the motion of a subject wearing the SAFER training unit. To collect data for your test, you have setup a small, motion tracking system. The tracking system uses magnetic markers on the SAFER and provides noisy measurements of the planar X and Y positions as well as a rotation angle, theta, of the SAFER. This problem explores the dynamics of this situation, simulates it and leads you through the development of a simple Kalman filter for tracking the position, velocity, angle and angular rate of a subject using this training version of the SAFER.
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Problems 1. Attach a local reference frame that rotates and translates with the subject on the SAFER (call this the “body frame”). Expressing the forces and torques in the body frame, derive the translational and rotational dynamics that describe the motion in the inertial reference frame . (You can assume that all forces and torques are applied through the center of mass of the subject / SAFER system). Justify any assumptions make regarding what effects to model and which ones you are leaving out.
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assign4_dynamics - SBE 2006 Dynamics Homework Problem...

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