This　paper　introduces　the　basic　Rapidly-Exploring　Random　Tree　(RRT)　and　its　basic　modification　Rapidly-Exploring　Random　Tree　star　(RRT∗),　which　is　not　only　the　extension　of　RRT,　but　also　a　widely　applied　algorithm　because　of　the　properties　of　asymptotically　optimal　path　regardless　of　any　obstacles,　whereas　the　limitation　to　achieve　optimal　path　has　a　slow　convergence　rate.　As　a　result,　it　costs　too　much　memory　and　time　due　to　a　large　number　of　iterations,　so　we　propose　a　method　that　should　change　the　sampling　scheme　from　random　distribution　sampling　to　Gaussian　distribution　sampling　to　overcome　this　limitation.　In　order　to　apply　the　improved　algorithm　in　robot　arms　or　manipulators　motion　planning,　we　extend　the　RRT∗　to　simulate　in　higher　dimensional　spaces,　the　planner　is　implemented　in　3D　workspace.　Finally　we　also　revise　the　Gaussian　distribution　to　suit　the　practical　environment.　©　2017　IEEE.