The　distributed　model　predictive　control　(DMPC)　strategy　with　particle　swarm　optimization　(PSO)　is　applied　to　solve　the　collision-free　trajectory　tracking　problem　for　the　mecanum-wheeled　mobile　robot　(MWMR)　formation.　Under　the　leader-follower　framework,　the　predictive　model　is　established　considering　the　kinematics　and　dynamics　of　the　MWMR　with　the　uncertainties　and　external　disturbances.　Based　on　the　information　from　itself　and　its　neighbors,　each　MWMR　is　assigned　its　own　finite-horizon　optimal　control　problem,　of　which　the　objective/cost　function　consists　of　formation　maintenance,　trajectory　tracking,　and　collision　avoidance　terms,　and　the　control　inputs　of　each　MWMR　are　computed　synchronously　in　a　distributed　manner.　PSO　serves　as　the　fast　and　effective　optimizer　to　find　feasible　solutions　to　these　finite-horizon　optimal　control　problems.　Further,　the　feedback　emendation　is　implemented　using　a　double　closed-loop　compensator　to　efficiently　inhibit　the　influence　of　unknown　dynamics　in　real　time.　The　stability　of　the　proposed　distributed　formation　control　approach　is　strictly　analyzed.　Numerical　simulations　confirmed　the　robustness　and　effectiveness　of　the　control　approach　in　obstacle　environments.