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111 this paper we prcsciit a n a.lgoritliiii for gcncratiiig iicar-tiiiicopt.iiiia.1 t.rajc.ctorics for a.n open-kincruatic-cli;lin iiinriipiilator i i i o v i i i g in a. cliitt.crctl workspace. This is tlic first algorithin 1.0 giiaraiitcc I~oiiiitls on the closciiess of a.n approxiiiia.tioii to a. t i m copt i i i i a l trajectory. The ruiuiiiig t,iiiie ancl space rcqriircd are polyiioiiiial iii { lie dcsirecl a.ccuracy of the approxiniatioii. The riscr niay also sp(xcify t.olcrniices I)y wliicli t lit. t.Ia jrctories iiiiist clrar o1)stacle.s in the worksince t,o a.llow iiiotleliiig of coiibrol errors. C!H2876-1/90/oooO/0150$01.~ 0 1990 IEEE

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