如图,四边形$ABCD$是正方形,曲线$DA_{1}B_{1}C_{1}D_{1}A_{2}\ldots$是由一段段$90$度的弧组成的.其中:$\widehat {D{A_1}}$的圆心为点$A$,半径为$AD$；$\widehat {{A_1}{B_1}}$的圆心为点$B$,半径为$BA_{1}$；$\widehat {{B_1}{C_1}}$的圆心为点$C$,半径为$CB_{1}$；$\widehat {{C_1}{D_1}}$的圆心为点$D$,半径为$DC_{1}$；$\widehat {D{A_1}}$,$\widehat {{A_1}{B_1}}$,$\widehat {{B_1}{C_1}}$,$\widehat {{C_1}{D_1}}\ldots$的圆心依次按点$A$,$B$,$C$,$D$循环.若正方形$ABCD$的边长为$1$,则$\widehat {{A_{2020}}{B_{2020}}}$的长是____.