+ Control of Spacecraft Relative Motion

Spacecraft relation motion refers to motion of spacecraft relative to another spacecraft or relative to some nominal orbital position. Spacecraft relative motion control problems include spacecraft rendezvous, docking, proximity operations and formation control.

Figure 1: Spacecraft relative motion control with debris avoidance.

In the ongoing research, control solutions based on model predictive control are being developed for the relative motion control of autonomous spacecraft subject to state and control constraints, including debris/obstacle collision avoidance. The constraints can be time-dependent representing moving debris or the effect of changing navigational uncertainty.

To facilitate real-time implementation on-board of the spacecraft, we focus on formulations which only require the solution of standard quadratic programming problems. To achieve this in the case of non-convex constraints, we use dynamically reconfigurable affine constraints to convexify the optimization problem.

Figure 2 illustrates an autonomous spacecraft performing a relative motion maneuver to move backward in an orbital track. The motion is visualized in a relative motion (Hill's) frame. The MPC controller generates an efficient trajectory subject to constraints on thrust. Note that the trajectory involves moving to higher radius orbit before descending back to the target which is more efficient than moving in a straight line and reduces spacecraft fuel consumption. Half way through the motion the spacecraft senses an obstacle, and MPC controller modifies the trajectory to avoid the obstacle. This trajectory is obtained experimentally in a robotic test-bed built to emulate the spacecraft motion. See the video of the experiment (Figure 3) and references for additional details.

Figure 2: Spacecraft relative motion maneuver with obstacle avoidance, generated by Model Predictive Controller applied to dynamically reconfigurable constraints. See references [3], [4] for details.

Experimental results have been obtained from a spacecraft robotic test-bed built to emulate the spacecraft motion. See the video below.

Figure 3: Video of relative motion control experiment, with spacecraft motion emulated by ground robots. See references [3], [4] for details.

More recently, we have been considering the application of techniques based on invariant and contractive sets for constrained spacecraft relative motion control with stationary and moving debris [3]. We have also treated combined translational and rotational relative motion control problems [4]. Figure 4 is a video of spacecraft docking to a rotating target where the maneuver is guided by a periodic reference governor. Finally, we have been developing strategies for constrained control of spacecraft formation. See Figure 5 and reference [7].

Figure 4: Periodic reference governor applied to control relative translational and rotational motion of spacecraft to dock with a rotating target. Left: Zoomed-out view. Right: Zoomed-in view. See reference [4] for details.

Figure 5: Time Shift Governor based control of two spacecraft to a target formation while satisfying thrust, collision avoidance and communication constraints. See reference [7] for details.

References:

[1] Di Cairano, S., Park, H., and Kolmanovsky, I.V., “Model predictive control approach to guidance of spacecraft rendezvous and proximity maneuvering,” International Journal of Robust and Nonlinear Control, Vol. 22, No. 12, pp. 1398-1427, August, 2012.

[2] Weiss, A., Baldwin, M., Erwin, R.S., Kolmanovsky, I.V., "Model Predictive Control for spacecraft rendezvous and docking: Strategies for handling constraints and case studies," IEEE Transactions on Control Systems Technology, Vol. 24, No. 4, pp. 1638-1647, June, 2015.

[3] Weiss, A., Petersen, C., Baldwin, M., Erwin R.S., and Kolmanovsky, I.V., “Safe positively invariant sets for spacecraft obstacle avoidance,” AIAA Journal of Guidance, Control, and Dynamics, Vol. 38, no. 4, pp. 720-732, 2015.

[3] C. Petersen, J. Pierre, C. Zagaris, M. Baldwin, and I.V. Kolmanovsky, “Hardware implementation of Model Predictive Control for relative motion maneuvering," Proceedings of 2015 American Control Conference, Chicago, IL, pp. 2311-2316, 2015.

[4] Petersen, C., and Kolmanovsky, I.V., “Coupled translational and rotational dynamics for precise constrained rendezvous and docking with periodic reference governors, Proceedings of 26th AAS/AIAA Space Flight Mechanics Meeting, Napa, CA, February 14-18, 2016, Advances in Astronautical Sciences, vol. 158, Paper AAS 16-507.

[5] Petersen, C., Jaunzemis, A., Baldwin, M., Holzinger, M.J., and Kolmanovsky, I.V., “Model Predictive Control and extended command governor for improving robustness of relative motion guidance and control,” AAS 14-249, Proceedings of AAS/AIAA Space Flight Mechanics Meeting, Santa Fe, NM, published in Advances in the Astronautical Sciences and Spaceflight Mechanics Volume 152, 2014.

[6] Park, H., Zagaris, C., Llop, V., Zappulla, R., Kolmanovsky, I.V., and Romano, M., “Analysis and experimentation of Model Predictive Control for spacecraft rendezvous and proximity operations with multiple obstacle avoidance,” Proceedings of

AIAA/AAS Astrodynamics Specialist Conference, Long Beach, California, doi 10.2514/6.2016-5273, AIAA Paper 2016-5273.

[7] Frey, G., Petersen, C., Leve, F., Garone, E., Kolmanovsky, I.V., Girard, A., “Time shift governor for coordinated control of two spacecraft formations, Proceedings of 2016 IFAC Symposium on Nonlinear Control System Design, Monterey, California, pp. 302-307, August, 2016.