Bio-inspired　jumping　robots　should　achieve　stable　jumping　in　field　environment.　Robots　easily　lose　stability　because　of　the　complex　terrain　and　large　speed　change.　Lateral　jumping　of　the　robot　with　four-bar　jumping　legs　under　rugged　terrain　was　used　as　the　research　object,　and　a　method　to　achieve　good　dynamic　stability　by　adjusting　the　leg　attitudes　of　the　robot　was　proposed.　The　stability　criteria　were　proposed　hierarchically　on　the　basis　of　the　analysis　of　the　jumping　mechanism　of　creatures.　Then,　the　dynamic　model　of　the　robot　jumping　on　the　slope　was　established,　and　the　effect　of　different　parameters　on　dynamic　stability　was　analyzed　to　carry　out　the　primary　selection　of　parameters.　Then,　the　method　of　maintaining　dynamic　stability　was　proposed.　On　the　basis　of　ensuring　large　motion　distances　and　stable　driving　torques,　leg　attitudes　were　considered　the　optimization　parameters.　Thus,　the　robot　does　not　overturn　or　turn　over　uncontrollably　in　the　take-off,　buffering,　and　flight　phases.　Analysis　results　of　robot　jumping　in　plane　and　3D　space　under　different　terrains　prove　the　feasibility　of　this　method.　In　particular,　the　dynamic　stability　of　the　robot　is　better　if　the　take-off　direction　is　considered　an　optimization　parameter.　The　simulation　results　also　proved　the　accuracy　of　the　analysis　results.　The　research　results　provide　a　theoretical　basis　to　realize　stable　continuous　jumping　of　bio-inspired　biped　robots.　©　2021