A　distributed　fault-tolerant　cooperative　scheme　for　nonholonomic　mobile　robots　under　a　directed　network　is　proposed　in　a　leader-follower　framework.　The　cooperative　scheme　consists　of　a　fault-tolerant　control　protocol　and　an　adaptive　estimation　of　actuator　fault　factor.　In　order　to　obtain　optimal　parameters,　a　sparrow　search　algorithm　is　combined　with　a　distributed　consensus　protocol.　Moreover,　the　designed　distributed　consensus　fault-tolerant　control　protocol　is　verified　by　seven　robots,　which　are　guaranteed　to　move　along　the　reference　trajectory　with　a　predefined　formation　pattern.　Finally,　the　simulation　results　show　that　the　control　performance　is　improved　with　the　optimized　parameters.　©　2022,　The　Author(s),　under　exclusive　license　to　Springer　Nature　Singapore　Pte　Ltd.