The　rapid　change　of　motion　direction　during　running　is　beneficial　to　improving　the　movement　flexibility　of　the　quadruped　robot,　which　is　of　great　relevance　to　its　research.　How　to　make　the　robot　change　its　motion　direction　during　running　and　achieve　good　dynamic　stability　is　a　problem　to　be　solved.　In　this　paper,　a　method　to　change　the　running　direction　of　the　cheetah-inspired　quadruped　robot　is　proposed.　Based　on　the　analysis　of　the　running　of　the　cheetah,　a　dynamic　model　of　the　quadruped　robot　is　established,　and　a　two-level　stability　index　system,　including　a　minimum　index　system　and　a　range　index　system,　is　proposed.　On　this　basis,　the　objective　function　based　on　the　stability　index　system　and　optimization　variables,　including　leg　landing　points,　trunk　movement　trajectory,　and　posture　change　rule,　are　determined.　Through　these　constraints,　the　direction　changes　with　good　dynamic　stability　of　the　cheetah-inspired　quadruped　robot　during　running　is　realized　by　controlling　the　leg　parameters.　The　robot　will　not　roll　over　during　high-speed　movement.　Finally,　the　correctness　of　the　proposed　method　is　proven　by　simulation.　This　paper　provides　a　theoretical　basis　for　the　quadruped　robot＇s　rapid　change　of　direction　in　running.