THE PROPOSED RESEARCH LOOKS TO DEVELOP THE MATHEMATICAL FRAMEWORK AND ALGORITHM FOR REAL-TIME ON-BOARD OPTIMAL GUIDANCE USING THE THEORY OF CONNECTIONS (A NEWLY ESTABLISHED TECHNIQUE TO SOLVE DIFFERENTIAL EQUATIONS). CURRENT PUBLICATIONS ON THE THEORY OF CONNECTIONS PROVIDE MACHINE-LEVEL ACCURATE SOLUTIONS IN MILLISECONDS. THIS PROVIDES A FOUNDATION FOR THE COMPUTATION OF DYNAMICAL EQUATIONS OF MOTION IN REAL-TIME IN ORDER TO MAKE CONTROL DECISIONS. MOREOVER A PRELIMINARY STUDY OF THIS TECHNIQUE APPLIED TO OPTIMAL GUIDANCE TYPE PROBLEMS HAS ALREADY BEEN CONDUCTED VALIDATING FURTHER WORK IN THIS AREA. WHILE THE MAIN GOAL OF THIS PROPOSAL IS TO DEVELOP A REAL-TIME OPTIMAL GUIDANCE ARCHITECTURE IT WILL ALSO FURTHER THE DEVELOPMENT OF THE THEORY OF CONNECTIONS AS A ROBUST MATHEMATICAL TOOL. IN GENERAL THIS HAS POTENTIAL TO BE APPLIED ACROSS ALL FIELDS OF ENGINEERING WHERE MACHINE LEVEL ACCURACY IS NECESSARY IN THE SOLUTION OF PROBLEMS. IN ALL RESEARCH IN REAL-TIME OPTIMAL GUIDANCE AND CONTROL IS THE BUILDING BLOCK FOR REDUCED RELIANCE ON EARTH BASED SYSTEMS FOR SPACEFLIGHT AND ULTIMATELY FULL SPACECRAFT AUTONOMY.