Fig. 1. Schematic diagram of Risley-prisms-based beam steering system. (a) Description of system parameters; (b) system arrangement

Fig. 2. Control singularity problem at center zone of field of regard (FOR) for real-time target tracking. (a) Schematic diagram for target moving at center zone of FOR; (b) variations of M required by real-time target tracking as a function of θ; (c) variations of maximum M value M_m as a function of Φ

Fig. 3. Schematic diagram of target tracking in discrete time domain

Fig. 4. Required rotation angle of two prisms for tracking target from point A (${\Phi }_A=\mathrm{1}°$, ${\Theta }_A=\mathrm{0}°$) to other points at center zone of FOR. (a) Required rotation angle $\mathrm{\Delta }{\varphi }_{\mathrm{1}}$ of prism I when adopting the same set of solutions; (b) required rotation angle $\mathrm{\Delta }{\varphi }_{\mathrm{1}}$ of prism I when switching solutions; (c) required rotation angle $\mathrm{\Delta }{\varphi }_{\mathrm{2}}$ of prism Ⅱ when adopting the same set of solutions; (d) required rotation angle $\mathrm{\Delta }{\varphi }_{\mathrm{2}}$ of prism Ⅱ when switching solutions

Fig. 5. Required values of ${\overline{M}}_{\mathrm{1}}$ and ${\overline{M}}_{\mathrm{2}}$ for tracking target from point A (${\Phi }_A=\mathrm{1}°$, ${\Theta }_A=\mathrm{0}°$) to other points at center zone of FOR. (a) Required values of ${\overline{M}}_{\mathrm{1}}$ when adopting the same set of solutions; (b) required values of ${\overline{M}}_{\mathrm{1}}$ when switching solutions; (c) required values of ${\overline{M}}_{\mathrm{2}}$ when adopting the same set of solutions; (d) required values of ${\overline{M}}_{\mathrm{2}}$ when switching solutions; (e) required values of ${\overline{M}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ when adopting the same set of solutions; (f) required values of ${\overline{M}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ when switching solutions

Fig. 6. Required values of ${\overline{M}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ for tracking target from point A (${\Theta }_A=\mathrm{0}°$) to other points at center zone of FOR by applying optimal-solution method. (a) ${\Phi }_A=\mathrm{1}°$; (b) ${\Phi }_A=\mathrm{0.5}°$; (c) ${\Phi }_A=\mathrm{0.1}°$; (d) variations of ${\overline{M}}_{\mathrm{M}}$ as a function of ${\Phi }_A$

Fig. 7. Sources of singularity problem for tracking target at center zone of FOR. (a) Schematic diagram for beam steering at center zone; (b) variations of difference between two sets of solutions as a function of $\Phi$

Fig. 8. Schematic diagram of tracking blind zone for rotational double prisms