THE PRIMARY GOAL OF THE PROPOSED EFFORT IS TO DEVELOP DUAL QUATERNION BASED METHODS AND ALGORITHMS TO SOLVE COMPLEX COUPLED 6-DEGREE-OF-FREEDOM (6-DOF) ROTATIONAL AND TRANSLATIONAL SPACE VEHICLE GUIDANCE PROBLEMS. MANY NASA MISSIONS CURRENT OR PLANNED REQUIRE COMPLEX GUIDANCE TRAJECTORIES TO ACHIEVE MISSION GOALS. CURRENT GUIDANCE APPROACHES RELY ON CLEVER ENGINEERING HEURISTICS AND EXTENSIVE PRE-MISSION PLANNING AND ANALYSIS AND HENCE THEY ONLY PROVIDE A LIMITED AUTONOMY WHICH IS SOMETIMES REFERRED TO AS MANAGED AUTONOMY. THE MAIN TECHNICALCHALLENGE IS THAT MOST OF THESE GUIDANCE PROBLEMS HAVE DEMANDING MISSION AND VEHICLE CONSTRAINTS AND REQUIREMENTS THAT MUST BE SATISFIED. HENCE THE RESULTING PROBLEMS ARE COMPLEX OPTIMIZATION PROBLEMS THAT ARE HARD TO SOLVE ESPECIALLY ONBOARD IN REAL-TIME. TO THIS END WE PROPOSE TO DEVELOP A DUAL QUATERNION BASED FORMULATION OF THE GUIDANCE PROBLEMS TO OBTAIN NUMERICALLY TRACTABLE OPTIMIZATION PROBLEMS WHOSE SOLUTIONS CAN BE COMPUTED ROBUSTLY ANDEFFICIENTLY. SPECIFICALLY THE RESULTING PROBLEMS WILL BE CONVEX OPTIMIZATION PROBLEMS WHOSE OPTIMAL SOLUTIONS CAN BE OBTAINED VERY RAPIDLY WITH DETERMINISTIC GUARANTEES. CONVEX OPTIMIZATION BASED ALGORITHMS HAVE RECENTLY BEEN DEMONSTRATED ON MARS PINPOINT LANDING POWERED DESCENT GUIDANCE PROBLEM IN ACTUAL FLIGHT TESTS AND PROVED TO BE AN ENABLING CAPABILITY. THOUGH THE PROPOSED EFFORT RELIES ON CONVEX OPTIMIZATION METHODS TO SOLVE GUIDANCE PROBLEMS IT IS FUNDAMENTALLY DIFFERENT AND NEW IN TWO KEY ASPECTS:I) THE PROPOSED EFFORT FOCUS ON A DIFFERENT CLASS OF APPLICATIONS NAMELY MOON OR PRIMITIVE LANDING MISSIONS (BOTH MANNED AND UNMANNED) WHERE THERE IS NO ENTRY PHASE AND MANY MISSION CONSTRAINT ARE 6-DOF COUPLED IN ATTITUDE AND TRANSLATION.II) WE UTILIZE DUAL QUATERNION FORMULATION RATHER THAN STANDARD SPACE VEHICLE STATES WHICH INHERENTLY COUPLES ATTITUDE AND TRANSLATIONAL MOTION. MOON AND PRIMITIVE BODY (COMETS AND ASTEROIDS) MISSIONS REQUIRE ACTIVE CONTROL THROUGHOUT THE PROXIMITY OPERATIONS. AS VEHICLES GET CLOSER TO THE SURFACE TERRAIN RELATIVE NAVIGATION (TRN)SENSORS SUCH AS THOSE DEVELOPED UNDER AUTONOMOUS LANDING AND HAZARD AVOIDANCE TECHNOLOGY (ALHAT) PROGRAM SHOULD BE ABLE TO OBSERVE THE LANDING SITE WHILE MANEUVERING [1]. HENCEATTITUDE POINTING CONSTRAINTS WILL BE COUPLED WITH THE POSITION OF THE VEHICLE RELATIVE TO THE SITE (WHICH IS A TRANSLATIONAL STATE). SUCH COUPLED TRANSLATIONAL AND ATTITUDE CONSTRAINTS ARE TYPICALLY STRONGLY NON-CONVEX IF THE STANDARD VEHICLE STATES ARE USED. ON THE OTHER HAND THE UTILIZATION OF DUAL QUATERNIONS TO DESCRIBE VEHICLE STATES NATURALLY ENABLE US TO FORMULATE THESE COMPLEX CONSTRAINTS AS CONVEX CONSTRAINTS ON THE SOLUTION VARIABLES. IN THIS PROJECT WE EMPLOY THE UNIT DUAL QUATERNION PARAMETERIZATION TO SIMULTANEOUSLY REPRESENT THE ORIENTATION AND POSITION OF THE SPACECRAFT AND PROPOSE THE ROTATIONALLY AND TRANSLATIONALLY CONSTRAINED ZONE FORMULATION WITH UNIT DUAL QUATERNION. INDEED THERE ARE SEVERAL KEY MISSION CONSTRAINTS ENCOUNTERED IN MANY SUCH APPLICATIONS. DUAL QUATERNION FORMULATIONS HOLD THE PROMISE OF NATURALLY CONVEXIFYING THESE INHERENTLY 6-DOF CONSTRAINTS THEREBY MOTIVATING THE PROPOSED RESEARCH EFFORT.