Real-time maneuver optimization of space-based robots in a dynamic environment: Theory and on-orbit experiments

Abstract This paper presents the development of a real-time path-planning optimization approach to controlling the motion of space-based robots. The algorithm is capable of planning three dimensional trajectories for a robot to navigate within complex surroundings that include numerous static and dynamic obstacles, path constraints and performance limitations. The methodology employs a unique transformation that enables rapid generation of feasible solutions for complex geometries, making it suitable for application to real-time operations and dynamic environments. This strategy was implemented on the Synchronized Position Hold Engage Reorient Experimental Satellite (SPHERES) test-bed on the International Space Station (ISS), and experimental testing was conducted onboard the ISS during Expedition 17 by the first author. Lessons learned from the on-orbit tests were used to further refine the algorithm for future implementations.

[1]  Suk-Hwan Suh,et al.  An algebraic approach to collision-avoidance trajectory planning for dual-robot systems: Formulation and optimization , 1992, Robotica.

[2]  Gamal N. Elnagar,et al.  The pseudospectral Legendre method for discretizing optimal control problems , 1995, IEEE Trans. Autom. Control..

[3]  D. Goldfarb A family of variable-metric methods derived by variational means , 1970 .

[4]  Alvar Saenz-Otero,et al.  AAS 09-011 SPHERES Demonstrations of Satellite Formations aboard the ISS , 2009 .

[5]  Larry Nazareth,et al.  A family of variable metric updates , 1977, Math. Program..

[6]  Daniel E. Koditschek,et al.  Exact robot navigation using artificial potential functions , 1992, IEEE Trans. Robotics Autom..

[7]  Steven M. LaValle,et al.  RRT-connect: An efficient approach to single-query path planning , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[8]  Lydia E. Kavraki,et al.  Anytime solution optimization for sampling-based motion planning , 2013, 2013 IEEE International Conference on Robotics and Automation.

[9]  Ben M. Chen,et al.  Minimum-time trajectory planning for helicopter UAVs using computational dynamic optimization , 2012, 2012 IEEE International Conference on Systems, Man, and Cybernetics (SMC).

[10]  George A. Boyarko,et al.  Rapid Path-Planning Options for Autonomous Proximity Operations of Spacecraft , 2010 .

[11]  Steven M. LaValle,et al.  Planning algorithms , 2006 .

[12]  Manuela M. Veloso,et al.  Real-Time Randomized Path Planning for Robot Navigation , 2002, RoboCup.

[13]  Marin Kobilarov Discrete geometric motion control of autonomous vehicles , 2008 .

[14]  M A Hurni,et al.  A Pseudospectral optimal motion planner for autonomous unmanned vehicles , 2010, Proceedings of the 2010 American Control Conference.

[15]  Byung Suk Lee,et al.  Automatic collision avoidance of ships , 2009 .

[16]  Jonathan P. How,et al.  Spacecraft trajectory planning with avoidance constraints using mixed-integer linear programming , 2002 .

[17]  Mark Campbell,et al.  On-Line Estimation and Path Planning for Multiple Vehicles in an Uncertain Environment , 2002 .

[18]  Stephen Kemble,et al.  Automated Rendezvous and Docking of Spacecraft , 2007 .

[19]  Antonio Bicchi,et al.  Conflict resolution problems for air traffic management systems solved with mixed integer programming , 2002, IEEE Trans. Intell. Transp. Syst..

[20]  Simon Nolet The SPHERES Navigation System: from Early Development to On-Orbit Testing , 2007 .

[21]  K.A. Morgansen,et al.  Decentralized reactive collision avoidance for multiple unicycle-type vehicles , 2008, 2008 American Control Conference.

[22]  Kris K. Hauser,et al.  An empirical study of optimal motion planning , 2014, 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[23]  C. G. Broyden The Convergence of a Class of Double-rank Minimization Algorithms 2. The New Algorithm , 1970 .

[24]  Emilio Frazzoli,et al.  Anytime Motion Planning using the RRT* , 2011, 2011 IEEE International Conference on Robotics and Automation.

[25]  I. Michael Ross,et al.  A unified computational framework for real-time optimal control , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[26]  I. Michael Ross,et al.  A review of pseudospectral optimal control: From theory to flight , 2012, Annu. Rev. Control..

[27]  C. G. Broyden The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations , 1970 .

[28]  Gregory E. Chamitoff Autonomous Guidance for the Recovery and Landing of a Remotely Piloted Vehicle , 1994 .

[29]  Anil V. Rao,et al.  ( Preprint ) AAS 09-334 A SURVEY OF NUMERICAL METHODS FOR OPTIMAL CONTROL , 2009 .

[30]  Sonia Cafieri,et al.  Aircraft deconfliction with speed regulation: new models from mixed-integer optimization , 2014, J. Glob. Optim..

[31]  R. Fletcher,et al.  A New Approach to Variable Metric Algorithms , 1970, Comput. J..

[32]  R. Olfati-Saber,et al.  Collision avoidance for multiple agent systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[33]  Guo-Jin Tang,et al.  Optimal Multi-Objective Nonlinear Impulsive Rendezvous , 2007 .

[34]  I. Michael Ross,et al.  Pseudospectral Optimal Control: A Clear Road for Autonomous Intelligent Path Planning , 2007, AIAA Infotech@Aerospace 2007 Conference and Exhibit.

[35]  Jonathan P. How,et al.  Cooperative path planning for multiple UAVs in dynamic and uncertain environments , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[36]  John T. Betts,et al.  Practical Methods for Optimal Control and Estimation Using Nonlinear Programming , 2009 .

[37]  Anil V. Rao,et al.  Algorithm 902: GPOPS, A MATLAB software for solving multiple-phase optimal control problems using the gauss pseudospectral method , 2010, TOMS.

[38]  Jonathan P. How,et al.  Safe Trajectories for Autonomous Rendezvous of Spacecraft , 2006 .

[39]  David W. Miller,et al.  SPHERES flight operations testing and execution , 2009 .

[40]  Behçet Açikmese,et al.  A mixed integer convex programming approach to Constrained Attitude Guidance , 2015, 2015 European Control Conference (ECC).

[41]  Marcello Romano,et al.  Flight Testing of Multiple-Spacecraft Control on SPHERES During Close-Proximity Operations , 2009 .

[42]  Steve Ulrich,et al.  Admissible Subspace TRajectory Optimizer (ASTRO) for Autonomous Robot Operations on the Space Station , 2014 .

[43]  Hui X. Li,et al.  A probabilistic approach to optimal robust path planning with obstacles , 2006, 2006 American Control Conference.

[44]  D. Shanno Conditioning of Quasi-Newton Methods for Function Minimization , 1970 .

[45]  David W. Miller,et al.  Development of a guidance, navigation and control architecture and validation process enabling autonomous docking to a tumbling satellite , 2007 .

[46]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[47]  Ahmad A. Masoud,et al.  Motion planning in the presence of directional and regional avoidance constraints using nonlinear, anisotropic, harmonic potential fields: a physical metaphor , 2002, IEEE Trans. Syst. Man Cybern. Part A.

[48]  David W. Miller,et al.  RESULTS OF SPHERES MICROGRAVITY AUTONOMOUS DOCKING EXPERIMENTS IN THE PRESENCE OF ANOMALIES , 2008 .

[49]  I. Michael Ross,et al.  Pseudospectral Motion Planning for Autonomous Vehicles , 2009 .

[50]  Bruce A. Conway,et al.  A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems , 2011, Journal of Optimization Theory and Applications.

[51]  Laureano F. Escudero,et al.  Collision Avoidance in Air Traffic Management: A Mixed-Integer Linear Optimization Approach , 2011, IEEE Transactions on Intelligent Transportation Systems.

[52]  Alvar Saenz-Otero,et al.  The SPHERES ISS Laboratory for Rendezvous and Formation Flight , 2003 .

[53]  K S Holt Development guidance. , 1979, Child: care, health and development.

[54]  Emilio Frazzoli,et al.  Distributed Control of Spacecraft Formations via Cyclic Pursuit: Theory and Experiments , 2010 .

[55]  Ping Lu,et al.  Autonomous Trajectory Planning for Rendezvous and Proximity Operations by Conic Optimization , 2012 .

[56]  Jean-Loup Farges,et al.  Hybridization of Nonlinear and Mixed-Integer Linear Programming for Aircraft Separation With Trajectory Recovery , 2013, IEEE Transactions on Intelligent Transportation Systems.