applied sciences  
A Parallel Robotic Antenna Design for Downlinking Leo Satellite Signal Subject to Wind Disturbance  
[PERSON] 1,*,+  
[PERSON] 2,++  
Footnote 1: email: [PERSON]. [PERSON], E.  
To maximize the downlink of the 2D beam signal within specifications, a smaller moving robotic antenna was considered [4] at the expense of increased complexity of the moving base due to the size and inertial of the antenna load. For full coverage, researchers proposed a parallel robot as the moving base but similar to the antenna, thus, imposing the tantamount task of dealing with nonlinear couplings at a dynamic level. Despite such apparent technical difficulties arising from a large parallel robot handling such antenna, these have been proven effective for downlink LEO satellites given that these are preferred over geostationary satellites due to the ground proximity, which enables short latency but, in contrast, introduces stringent tracking requirements to the Earth station along the short passage flying time. Moreover, the Gough-Stewart platform (GS) has been proposed to this end, becoming a robotic base that yields an active antenna tracking the 2D beam slice; however, the large antenna plate induces a state-dependent persistent aerodynamic wind disturbance into the dynamical system. Consequently an integrated design of the GS platform with the antenna structure is required to address properly the problem of downlink LEO satellite signals at different Earth's longitude and latitude. The high stiffness-to-load ratio of GS platforms has become the choice over serial ones, given the large antenna size, of high mass and inertia, the challenge goes beyond integrated design with the antenna but the controller to track a two-DoF trajectory in different Earth locations. Since the beam satellite trajectory lies over a virtual spherical constraint (see Figure 2) a six-DoF parallel robot is suggested to maneuver in its reachable workspace. Although the modeling and control for the GS is well understood, the challenge to design and control a parallel robot handling the antenna load under induced disturbances, to track a two-DoF trajectory over a virtual spherical constraint, has not been addressed in the literature. Moreover, the latency and path specifications are critical; thus, the motion planner of georeferenced paths is also an integral part of the problem. In this paper, we aim at solving this problem for a point-to-point tracking scheme with a simple and easy to implement  
Figure 2: Parabolic antenna mounted on a Gough–Stewart platform. This shows three poses corresponding to the antenna focus at three locations onto a virtual spherical motion constraint. controller that meets the specifications for the downlink signal, yet exhibits some robustness against unavoidable aerodynamic (wind) disturbances. The large body of literature on modeling and control of GS parallel robot deserve further discussion given the plethora of studies for a variety of applications; however, the design at the dynamic level is missing for antenna pointing with high loads and state-dependent disturbances. Nevertheless, several nonlinear controllers have addressed the tracking of the GS robot under ideal conditions neglecting the antenna load but not for pointing at passive LEO satellite orbits nor subject to state-dependent disturbances, let alone with an online motion planner for this case. Interestingly, Ref. [5] models the Euler-Lagrange platform under a nominal Computed Torque plus PID and friction estimation, without disturbances neither any antenna load nor pointing. In [6], sensitivity analysis of the inertial coupling of a moving base along a space constraint is presented; however, the structural mechanical analysis of limb control is limited to the linear domain, while [7] proposed a conventional model-based adaptive control assuming simplified dynamics, under ideal tracking conditions.