This　paper　deals　with　leader-follower　formation　control　of　mobile　robots,　including　a　leader　robot　trajectory　tracking　strategy　and　a　follower　robot　formation　maintaining　strategy.　Robots＇　control　inputs　are　limited　to　satisfy　practical　constraints　that　restrict　the　range　of　feasible　leader　paths　and　possible　positions　of　the　follower　with　respect　to　the　leader.　First,　a　backstepping　control　method　is　used　to　develop　a　trajectory　tracking　controller　that　enables　the　leader　robot　to　track　the　desired　formation　trajectory　quickly.　Then,　a　Nonlinear　Model　Predictive　Control　(NMPC)　technique　is　employed　to　transform　the　formation　dynamics　of　the　follower　robots　into　a　quadratic　programming(QP)　optimization　problem　with　velocity　constraints.　In　order　to　effectively　tackle　the　optimization　problem,　a　Primal-Dual　Neural　Network　(PDNN)　solver　is　implemented　to　obtain　the　optimal　solution.　Finally,　numerical　simulations　are　demonstrated　to　validate　the　effectiveness　of　the　proposed　formation　control　method.　©　2022　IEEE.