Control　synthesis　and　reachability　analysis　of　the　piecewise　affine　hybrid　systems　on　simplices　were　applied　for　safely　steering　a　robot　from　a　given　position　to　a　final　position　with　consideration　of　optimality.　Based　on　the　triangulation　of　the　state　space　of　a　robot,　a　dual　graph　was　constructed　following　the　target　attractive　principle,　and　then　a　path　planning　algorithm　was　presented　to　find　a　sequence　of　adjacent　triangles　that　were　traversed　by　the　shortest　path.　According　to　the　characteristics　of　affine　systems　on　simplices,　a　motion　planning　algorithm　was　proposed　to　determine　the　translational　and　rotational　velocities　for　a　robot.　The　simulation　results　demonstrate　the　effectiveness　of　the　algorithms.