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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