Sufficient conditions for the lipschitz continuity of QP-based multi-objective control of humanoid robots

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2013, Pages 2920-2926

  Morris, Benjamin ^a   Powell, Matthew J ^a   Ames, Aaron D ^a  

^a Texas AandM University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPLICATION PROGRAMS; LYAPUNOV FUNCTIONS; QUADRATIC PROGRAMMING;

CONTINUITY PROPERTIES; CONTROL LYAPUNOV FUNCTION; FEEDBACK CONTROLLER; LIPSCHITZ CONTINUITY; MULTI-OBJECTIVE CONTROL; QUADRATIC PROGRAMS; SIMULATION STUDIES; STATE-DEPENDENT;

ANTHROPOMORPHIC ROBOTS;

EID: 84902338727     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2013.6760327     Document Type: Conference Paper

References (23)

1. Yeuhi Abe, Marco da Silva, and Jovan Popoviv́. Multiobjective control with frictional contacts. In Eurographics/ACM SIGGRAPH Symposium on Computer Animation, 2007.
2. Tamas Terlaky, Alireza Ghaffari Hadigheh, and Oleksandr Romanko. Sensitivity analysis in convex quadratic optimization: Simultaneous perturbation of the objective and right-hand-side vectors. Algorithmic Operations Research, 2(2), 2007.
3. A. D. Ames, K. Galloway, and J. W. Grizzle. Control Lyapunov Functions and Hybrid Zero Dynamics. Proc. 51st IEEE Conf. Decision and Control, 2012.
4. A. D. Ames, K. Galloway, J. W. Grizzle, and K. Sreenath. Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics. Conditionally Accepted to IEEE Trans. Automatic Control, 2012.
5. A. D. Ames and Matthew Powell. Towards the unification of locomotion and manipulation through control lyapunov functions and quadratic programs. In Control of Cyber-Physical Systems, Lecture Notes in Control and Information Sciences, 449:219-240, 2013.
6. Alberto Bemporad, Manfred Morari, Vivek Dua, and Efstratios N. Pistikopoulos. The explicit solution of model predictive control via multiparametric quadratic programming. In Proceedings of the American Control Conference, 2012.
7. J. Frederic Bonnans and Alexander Shapiro. Perturbation Analysis of Optimization Problems. Springer, 2000.
8. M. R. Davidson. Stability of the extreme point set of a polyhedron. Journal of Optimization Theory and Appl., 90(2):357 - 380, 1996.
9. R. A. Freeman and P. V. Kokotović. Robust Nonlinear Control Design. Birkhüser, 1996.
10. Grant N. Galbraith and Richard B. Vinter. Lipschitz continuity of optimal controls for state constrained problems. SIAM J. CONTROL OPTIM., 42(5):1727-1744, 2003.
11. Kevin Galloway, Koushil Sreenath, Aaron D. Ames, and J. W. Grizzle. Torque saturation in bipedal robotic walking through control lyapunov function based quadratic programs. Technical report, http://arxiv.org/abs/1302.7314 2013.
12. O. Khatib. A unified approach for motion and force control of robot manipulators: The operatoinal space formulation. IEEE Journal of Robotics and Automation, 3:43-53, 1987.
13. O. L. Mangasarian and S. Fromovitz. The fritz john necessary optimality conditions in the presence of equality and inequality constraints. Journal of Mathematical Analysis and Applications, 17:37-47, 1967.
14. Jacob Mattingley and Stephen Boyd. Cvxgen: A code generator for embedded convex optimization. Optimization and Engineering, 13(1):1-27, 2012.
15. H. X. Phu and N. D. Yen. On the stability of solutions to quadratic programming problems. Mathematical Prog., 89:385-394, 2001.
16. Stephen M. Robinson. Stability theory for systems of inequalities. part i: Linear systems. SIAM Journal on Numerical Analysis, 12(5):754 - 769, 1975.
17. Stephen M. Robinson. A characterization of stability in linear programming. Operations Research, 25:435 - 447, 1977.
18. S. Sastry. Nonlinear Systems: Analysis, Stability and Control. Springer Verlag, 1999.
19. Bruno Siciliano and Jean Jacques E Slotine. A general framework for managing multiple tasks in highly redundant robotic systems. In Fifth International Conference on Advanced Robotics (ICAR), 1991.
20. E. Sontag. A 'universal' contruction of Artstein's theorem on nonlinear stabilization. Systems & Control Letters, 13:117-123, 1989.
21. Benjamin J. Stephens and Christopher G. Atkeson. Push recovery by stepping for humanoid robots with force controlled joints. In IEEE International Conference on Humanoid Robots, 2010.
22. Russ Tedrake, Ian R. Manchester, Mark Tobenkin, and John W. Roberts. Lqr-trees: Feedback motion planning via sums of squares verification. International Journal of Robotics Research, 29:1038- 1052, 2010.
23. E. R. Westervalt, J. W. Grizzle, C. Chevallereau, J. H. Choi, and B. Morris. Feedback Control of Dynamic Bipedal Robot Locomotion. Taylor & Francis/CRC, 2007.