Work

Fast Trajectory Optimization via Successive Convexification for Spacecraft Rendezvous with Integer Constraints

Year: 2020

Type: conference-paper

Abstract: In this paper we present a fast method based on successive convexification for generating fuel-optimized spacecraft rendezvous trajectories in the presence of mixed-integer constraints. A recently developed paradigm of state-triggered constraints allows engineers to efficiently embed a subset of discrete decision constraints into the continuous optimization framework of successive convexification. As a result, difficult trajectory optimization problems can be solved at interactive speeds unattainable by a mixed-integer programming approach that would require significantly more solution time and computing power. Our method is applied to the real problem of transposition and docking of the Apollo command and service module with the lunar module. We demonstrate that, within seconds, we are able to obtain trajectories that are up to 90 percent more fuel efficient (saving up to 45 kg of fuel) than non-optimization based Apollo-era design targets. Our trajectories take explicit account of minimum thrust pulse width and plume impingement constraints. Both of these constraints are naturally mixed-integer, but we handle them as state-triggered constraints. Our algorithm can serve as a useful off-line design tool for rapid trajectory trade studies.

Source: AIAA SciTech Forum

DOI: 10.2514/6.2020-0616

Authors: Danylo Malyuta, Taylor Reynolds, Michael Szmuk, Behcet Acikmese, Mehran Mesbahi

Institution: University of Washington

Language: English

Topic: Spacecraft Dynamics and Control

Subfield: Aerospace Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Aeronautics and Space Administration, Division of Civil, Mechanical and Manufacturing Innovation

Awards: 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., CAREER: Real-time Convex Optimization for High-Performance Control of Autonomous Systems