Lie Group Observer Design for Robotic Systems: Extensions, Synthesis, and Higher-Order Filtering

David Zlotnik
Aerospace Engineering PhD Candidate

Prof. James R. Forbes
Dissertation Chair

Lie groups, a class of differential manifold with a group structure, arise naturally in the study of rigid-body kinematics. This dissertation studies the design of state observers for systems whose state evolves on a Lie group. State observers, or state estimators, are a crucial part of the navigation algorithms necessary for autonomous operation of robotic systems. One such nonlinear observer, the gradient-based observer, has generated significant interest in the literature due to its computational simplicity and stability guarantees. The first part of this dissertation explores several applications of the gradient-based observer, including both the attitude estimation problem and the simultaneous localization and mapping (SLAM) problem.

In addition, state of the art in Lie group observer design is extended by the development of a higher-order filter on a Lie group. By analogy to the classical linear complementary filter, the proposed method can be interpreted as a nonlinear complementary filter on a Lie group. A disturbance observer that accounts for constant and harmonic disturbances in the group velocity measurements is also considered. Local asymptotic stability about the desired equilibrium point is demonstrated. In addition, an H2-optimal filter synthesis method is derived and disturbance rejection via the internal model principle is considered.

Publications

Journal Publications

Zlotnik, D. E., and Forbes, J. R., "Higher-Order Nonlinear Complementary Filtering on Lie Groups,'' IEEE Transactions on Automatic Control, 2018.

Zlotnik, D. E., and Forbes, J. R., "Gradient-Based Observer for Simultaneous Localization and Mapping,'' IEEE Transactions on Automatic Control, 2018.

Zlotnik, D. E., and Forbes, J. R., "Exponential Convergence of a Nonlinear Attitude Estimator,'' Automatica, vol. 72, pp. 11-18, 2016.

Zlotnik, D. E., and Forbes, J. R., "Nonlinear Estimator Design on the Special Orthogonal Group using Vector Measurements Directly,'' IEEE Transactions on Automatic Control, 2016.

Caverly, R. J., Zlotnik, D. E., and Forbes, J. R. "Saturated Control of Flexible-Joint Manipulators Using a Hammerstein Strictly Positive Real Compensator,'' Robotica, 2014

Forbes, J. R., de Ruiter, A. H., Zlotnik, D. E. "Continuous-Time Norm-Constrained Kalman Filtering,'' Automatica, vol. 50, no. 10, pp. 2546–-2554, 2014.

Zlotnik, D. E., and Forbes, J. R., "Dynamic Modelling, Estimation, and Control for Precision Pointing of an Atmospheric Balloon Platform, "Transactions of the Canadian Society for Mechanical Engineering, Vol. 38, No. 2, pp. 263-274, 2014, invited submission.

Caverly, R. J., Zlotnik, D. E., and Forbes, J. R. "Saturated Proportional Derivative Control of a Single-Link Flexible-Joint Manipulator,'' Transactions of the Canadian Society for Mechanical Engineering, Vol. 38, No. 2, pp. 241-250, 2014, invited submission.

Caverly, R. J., Zlotnik, D. E., L. J. Bridgeman and Forbes, J. R. "Saturated Proportional Derivative Control of Flexible-Joint Manipulators,'' Robotics and Computer Integrated Manufacturing. Vol. 30, No. 6, 658-666, 2014.


Conference Publications

Zlotnik, D. E., Di Cairano, S., and Weiss, A., "MPC for coupled station keeping, attitude control, and momentum management of GEO satellites using on-off electric propulsion,'' 2017 IEEE Conference on Control Technology and Applications (CCTA), Mauna Lani, HI, 2017, pp. 1835-1840

Zlotnik, D. E., and Forbes, J. R., "Exteroceptive measurement filtering embedded within an SO(3)-based attitude estimator,'' Proc. of the Conference on Decision and Control, Las Vegas, NV, USA, December 12-14, 2016.

Zlotnik, D. E., Forbes, J. R., and Aldrich, J., ``Control Bandwidth Recovery of Flexible Pointing Systems,'' Proc. of the American Control Conference, Boston, MA, USA, July 6-8, 2016.

Zlotnik, D. E., and Forbes, J. R., "A Nonlinear Attitude Estimator with Desirable Convergence Properties,'' Proc. of the European Control Conference, Linz, Austria, July 15-17, 2015.

Zlotnik, D. E., and Forbes, J. R., "Effect of Pendulation on an SO(3)-Based Attitude Estimator for Precision Pointing of an Atmospheric Balloon-Borne Platform,'' AHAC Academic High Altitude Conference, Grand Forks, ND, USA, June 24-27, 2014.

Zlotnik, D. E., and Forbes, J. R., "Rotation-Matrix-Based Attitude Control Without Angular Velocity Measurements," American Control Conference, Portland, OR, USA, June 4-6, 2014.

Tran, N. K., Zlotnik, D. E., and Forbes, J. R., "Design of an Attitude Control System for a High-Altitude Balloon Payload'', AHAC Academic High Altitude Conference, Upland, IN, USA, June, 2013.

Zlotnik, D. E., and Forbes, J. R., "Dynamic Modelling, Estimation, and Control for Precision Pointing of an Atmospheric Balloon Platform," CCToMM M3 Symposium, Montreal, QC, Canada, May 30-31, 2013.

Caverly, R. J., D. E.Zlotnik, and Forbes, J. R., "Saturated Proportional Derivative Control of a Single-Link Flexible-Joint Manipulator," CCToMM M3 Symposium, Montreal, QC, Canada, May 30-31, 2013.

Tran, N.~K., He, X., Zlotnik, D. E., and Forbes, J. R., "Attitude Sensing and Control of a Stratosphere Balloon Platform,'' AIAA Aerodynamic Decelerator Systems Technology Conference, Daytona Beach, FL, USA, March, 2013.