The　real-time　and　reliable　collision　detection　is　the　vital　basis　for　the　robotic　motion　control　in　real　applications.　In　this　work,　the　minimal　distance　calculation　between　the　industrial　robot　and　its　workspace　is　presented.　This　method　first　uses　circular/polygonal　slices　to　represent　robotic　sub-structures　with　curved　edges　more　accurately,　and　uses　polygonal　planes　to　construct　its　workspace.　Being　the　basis　of　the　distance　calculation,　the　shortest　distance　between　the　spatial　circle/polygon　and　the　polygonal　plane,　as　well　as　that　between　the　circular/polygonal　plane　and　the　polygonal　plane　are　first　modelled　through　spatial　relation　analysis.　The　simulation　validation　indicates　that　the　proposed　algorithm　is　more　efficient　and　reliable　than　both　the　point-clouds-based　and　bounding-volume-hierarchies-based　algorithms.　And　the　influence　of　the　refinement　size　on　the　performance　of　the　proposed　model　is　revealed.　Finally,　the　application　example　shows　that　this　work　is　a　significant　contribution　for　the　collision-free　motion　control　of　the　industrial　robot.　The　proposed　algorithm　can　also　be　applied　to　the　distance　calculation　of　other　complex　objects　because　of　the　generality　of　the　proposed　slices　representation　way.　(C)　2020　Elsevier　Inc.　All　rights　reserved.