Autonomous Guidance for Asteroid Descent using Successive Convex Optimization

Kurzfassung

With the onset of the age of space travel, asteroid missions have been steadily gaining interest. The pristine nature of asteroids due to their preserved state since the formation of the Solar System is an opportunity to unravel many mysteries about the Solar System. Also with the ever-growing need for resources, asteroids prove to be a plentiful source. With the discovery of asteroids in the close vicinity of our planet and a probable threat to the preservation of life, a need for defence missions has also arisen. With many successful missions like NEAR to Eros, Rosetta to Comet 67P, Hayabusa to Itokawa, Hayabusa 2 to Ryugu, OSIRIS-REx to Bennu, etc., the requirement of precise navigation with autonomous guidance and control for future missions has been established. The ever-growing need for better computational speed and accuracy has led to the development of new representations for attitude and position of the spacecraft in the past. The usual methods of representations of position and attitude (pose) are the Cartesian coordinates and quaternions. A recent development is the simultaneous representation of the pose of the spacecraft using dual quaternions which are eight-dimensional vectors. As of February 2019, a variety of missions using dual quaternions for relative navigation, rendezvous and docking, entry, descent and landing have been conceptualised. Recent studies have narrowed down from the existing guidance algorithms to, Successive Convexification and Sampling Based Model Predictive Optimisation, as future prospects for autonomous guidance of missions. These missions are limited by the lack of instantaneous ground control due to operations at very far distances from Earth. In this thesis, an attempt to incorporate these state-of-the-art guidance technologies to asteroid missions has been made. The novelty in this thesis is, using dual quaternions for SC pose and attitude representation to autonomously guide the spacecraft for mapping an asteroid and perform a touch and go descent using sampling-based motion predictive optimisation and successive convexification respectively. To achieve this objective, this thesis first browses through past missions to establish the requirements of a mission to asteroids. Then it explores the augmented algebra of dual numbers and their application in the concept of dual quaternions. It then works towards establishing the dynamics and kinematics in the asteroid centred rotating frame using dual quaternions along with modelling the environment around the asteroids. This thesis delves into the method of convex optimisation to present its existing algorithms and develop a dynamic successive convex optimisation method to achieve better results as compared to the method developed by Mao et al. (2016). The thesis establishes the initialisation of a sampling-based model predictive optimisation method for autonomous mapping of a target asteroid. After the development and verification of these algorithms, different scenarios have been designed to find out the robustness of the dynamic successive convexification method. The scenarios have been run by both the Cartesian quaternion and dual quaternion based algorithms. They are found to behave similarly in their results, besides the latter being computationally more expensive as proved by different theses so far. The algorithm performs better than the one developed by Szmuk et al. (2017), but faces difficulties with badly scaled problems as is the nature of missions to asteroids. The software used for the thesis is ECOS, which faces numerical problems in these mission scenarios even when the problem is feasible and has an optimal result. The availability of a solution to the optimal control problem depends on the scaling of the penalty weights used in the cost function to penalise virtual controls and trust region, which are used to prevent infeasibility and bound the problem, respectively. It also depends on finding an appropriate final time for the descent along with the number of nodes for discretisation. This research proves, that successive convexification indeed provides a speedy solution for an autonomous precision descent but needs further work to make it robust and stable. The outcome of this thesis is to carry out further research to understand the complex relations, between the scale of the problem, simulation parameters for the optimal control problem and final time in order to make the algorithm robust and safe for an autonomous mission. Another important future research prospect is to incorporate the sampling based model predictive optimisation, for the SC to autonomously map the target body and help in selecting a landmark for a descent