23 April 2010 Weighted least-squares based control for a four axis gimbal set
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Gimbal lock is a phenomenon which occurs in multi-gimbaled systems when two axes are driven into a coplanar orientation, thereby resulting in the loss of one degree of rotational freedom. This paper presents a control scheme which introduces a redundant fourth axis in conjunction with an algorithm that minimizes weighted least-square gimbal rates, ultimately permitting the use of open inner and middle gimbals to achieve a wide field of view. The control algorithm produces a singularity/gimbal lock measure which is derived using the inner three gimbals, and used to adapt the weights and transition the table from three-axis operation to four-axis operation at or near the three-axis gimbal lock orientation. Weight adaptation minimizes the peak gimbal rate required to track a vehicle reference rate profile. The control strategy also minimizes tracking errors between vehicle kinematic motion,which is obtained from the vehicle dynamics simulation, and kinematic motion induced onto the table-mounted payload. The control algorithm accepts Euler angles and body rates, as defined in the body fixed frame of reference, and generates four gimbal command sets. Each gimbal command set consists of gimbal acceleration, rate, and angle. Mathematical analysis, simulation, and 3-D CAD multi-body dynamics visualizations are included, illustrating differences between desired vehicle kinematic motion and that induced by this control strategy onto the table mounted payload, including an examination of effects due to finite gimbal control loop bandwidths.
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Delano R. Carter, Delano R. Carter, Patrick Duffey, Patrick Duffey, Steve Bachorski, Steve Bachorski, Martin Kägi, Martin Kägi, Howard Havlicsek, Howard Havlicsek, } "Weighted least-squares based control for a four axis gimbal set", Proc. SPIE 7663, Technologies for Synthetic Environments: Hardware-in-the-Loop Testing XV, 76630I (23 April 2010); doi: 10.1117/12.851344; https://doi.org/10.1117/12.851344


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