A　mobile　manipulator　typically　consists　of　a　mobile　platform　and　a　robotic　manipulator　mounted　on　the　platform.　The　base　placement　of　the　platform　has　a　great　influence　on　whether　the　manipulator　can　perform　a　given　task.　In　view　of　the　issue,　a　new　approach　to　optimize　the　base　placement　for　a　specified　task　is　proposed　in　this　paper.　Firstly,　the　workspace　of　a　redundant　manipulator　is　investigated.　The　manipulation　capability　of　the　redundant　manipulator　is　maximized　based　on　the　manipulability　index　through　the　joint　self-motion　of　the　redundant　manipulator.　Then　the　maximum　manipulation　capability　in　the　specified　work　point　is　determined.　Next,　the　relative　manipulability　index　(RMI)　is　defined　for　analyzing　manipulation　capability　of　the　manipulator　in　its　workspace,　and　the　global　manipulability　map　(GMM)　is　presented　based　on　the　above　measure.　Moreover,　the　optimal　base　placement　related　to　the　given　task　is　obtained,　and　the　motion　planning　is　implemented　by　an　improved　rapidly-exploring　random　tree　(RRT)　algorithm　with　the　RMI,　which　can　enhance　the　manipulation　capability　from　the　initial　point　to　the　target　point.　Finally,　the　feasibility　of　the　proposed　algorithm　is　illustrated　with　numerical　simulations　and　experiments　on　the　mobile　manipulator.