Preliminary Results on Waypoint Tracking for Spacecraft with Actuator Constraints Espen Oland Department of Electrical Engineering UiT - The Arctic University of Norway Narvik, Norway espen.oland@uit.no Tom Stian Andersen Department of Electrical Engineering UiT - The Arctic University of Norway Narvik, Norway tom.s.andersen@uit.no Abstract—This paper presents preliminary results on how to perform waypoint tracking with spacecraft with actuator constraints. It considers a simplified spacecraft model and can be considered a deep space model, and shows how to perform waypoint tracking with only one main thruster together with full attitude control. As the spacecraft reaches close to the waypoint during a deceleration phase that makes the speed go towards zero, reaction control thrusters are used to make the remaining velocity error go to zero achieving the control objective. Keywords—Rendezvous, waypoint tracking, spacecraft, actua- tor constraints I. I NTRODUCTION The rendezvous problem was ranked first among the top technology challenges in the 2011 technology roadmap by NASA on the topic of ”Robotics, Tele-Robotics, and Au- tonomous Systems” [1]. To that end there is a need for research on this topic, which is important to pave the way for future space exploration. One of the most basic problems is to perform a translational motion from a point A to a point B. Assuming a fully actuated vehicle with full translational control in all axes, this can easily be achieved using a standard PID controller using position feedback. By including actuator constraints this becomes a little more involved. From a design point of view, it does not make sense to fit a spacecraft with large translational thrusters along each axis, such that the most natural design will include one main thruster together with attitude control actuators (e.g. reaction wheels) as well as reaction control thrusters for station-keeping and small translational maneuvers. This means that in order to perform a translational maneuver from a point A to point B using one main thruster, the first objective is to point the thrust direction towards the waypoint. Then after accelerating to a desired velocity (or simply for a given time), the spacecraft must be rotated 180 ◦ such that the thruster points along the direction of motion and must be used to decelerate until the waypoint is reached. For terrestial waypoint tracking in cases such as unmanned aerial vehicles (UAVs), aircraft, ships, and underwater vehicles, there will always be a convenient viscous damping that helps controlling the speed and bounding the velocity components during the maneuver. In space, nothing helps you brake; such that special maneuvers are required to achive the control objective. The topic of waypoint tracking has received much attention throughout the ages with applications such as ships [2], aircraft [3], underwater vehicles [4], UAVs [5], missiles [6], as well as spacecraft [7], [8], [9], [10]. Phillips et al. show in [7] how to perform close proximity maneuvers while accounting for propellant impingement. This is achieved using a series of waypoints that is tracked by a fully actuated spacecraft. Guo et al. show in [8] how to perform a waypoint-optimized Mars landing and the authors apply the Zero-Effort-Miss/Zero-Effort-Velocity method and account for nonlinear actuator constraints. Furfaro and Linares apply in [9] the ZEM/ZEV feedback approach in conjunction with reinforcement learning to perform obtain a precise planetary landing. In many ways, the problem of performing a precise landing can be considered similar to the problem of performing waypoint tracking with constrained actuation. This paper builds on the previous research mentioned above, as well as work performed by the authors [5], which show how to perform waypoint tracking and collision avoidance by properly defining desired orientation parameterized as quater- nions. This approach is here applied for waypoint guidance for spacecraft. This paper is structured as follows: Section II presents the modeling used in this paper, where the spacecraft dynamics is simplified. Section IV explains the main ideas of finding the desired orientation and how to perform the waypoint maneuvers. Section V detail the controllers used in this work. Section VI presents simulations of a spacecraft that tracks a series of waypoints using one main thruster for large translational maneuvers, where small reaction control thrusters are activated close to the waypoint. The paper is then wrapped up with a conclusion discussing the results, and future work. A. Problem Statement Given a spacecraft with one main thruster for translational control, reaction wheels for attitude control and reaction control thrusters for final position control, design a guidance and control system that enables the spacecraft to track a series of waypoints.