ESA GNC Conference Papers Repository

Convex guidance, navigation, and control for pin-point lunar landing
K. de Ridder , E. Mooij
Presented at:
Salzburg 2017
Full paper:

Throughout the decades of space exploration, many soft landings have been performed on different bodies in the Solar System. Because traditional landers could be off by kilometres from their original targets, they were sent to relatively low-risk landing locations. However, to improve scientific return or to study specific geological features, new missions should be able to target more diverse landing environments. Therefore, modern landers require a much higher precision to land. For ESA's Lunar Lander and NASA's Altair, for example, the landing-precision requirement was speci?ed to be within a few hundred metres of the initially targeted landing site. Because this range includes possible retargeting after hazard identification, the allowed uncertainty at touch-down is even more restricted. Possible hazards near the landing site and the requirement to always have the landing site within the field of view of the spacecraft's sensors highly constrain the landing trajectory. Convex guidance is a developing guidance algorithm that can optimise the aforementioned highly constraint landing trajectories quickly and efficiently. The algorithm utilises convex optimisation to guarantee convergence to the global optimum in the design space. This makes the algorithm very well suited for on-board trajectory optimisation of autonomous landers. For example, if during the landing a hazard is detected near the landing site, the landing trajectory can be re-optimised given the additional constraint. Or alternatively, if the decision is made to divert to another landing site, convex guidance can determine the optimal trajectory to this new landing site from the spacecraft's current location. Most studies into new guidance algorithms assume instantaneous attitude control and perfect state knowledge. Therefore, to complement this body of knowledge, this study investigates the practical application of convex guidance in a full guidance, navigation and control (GNC) loop for a Lunar landing with realistic spacecraft dynamics. This study found several mathematical simplifications to Convex Guidance that reduced the computational time of the algorithm without negatively impacting its performance. Furthermore, the problem is transcribed to conical form, significantly reducing the required computational time, and thereby improving its potential for on-board use on a spacecraft even further. Besides these fundamental changes to the algorithm, a detailed overview is given of the error contributions caused by mathematical simplifications and neglected effects, like discretisation, Lunar rotation, third body perturbations and irregularities in the Lunar gravity field. In the case of significant error contributions, small changes to the guidance algorithm are proposed to improve its performance. On a practical level, this study shows that convex guidance performs very well in a GNC loop that requires the ability to re-optimise the landing trajectory on the fly. In combination with the upcoming generation of visual navigation sensors, a spacecraft should be able to land within the order of metres. However, because no attitude dynamics are modelled by convex guidance, large attitude discontinuities can occur during the landing, and no initial- or ?nal-boundary attitude conditions can be imposed. Therefore, two different methods are proposed to introduce an angular-rate-limiter in the guidance loop.