Chapter 15 System Theory and Analytical Techniques

[1]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[2]  K. Lynch Nonholonomic Mechanics and Control , 2004, IEEE Transactions on Automatic Control.

[3]  V. Boltyanskii Sufficient Conditions for Optimality and the Justification of the Dynamic Programming Method , 1966 .

[4]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[5]  Florent Lamiraux,et al.  Flatness and small-time controllability of multibody mobile robots: Application to motion planning , 1997, 1997 European Control Conference (ECC).

[6]  H. Hermes,et al.  Nilpotent bases for distributions and control systems , 1984 .

[7]  L. Grüne An adaptive grid scheme for the discrete Hamilton-Jacobi-Bellman equation , 1997 .

[8]  M. Rathinam,et al.  Configuration flatness of Lagrangian systems underactuated by one control , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[9]  H. Sussmann,et al.  A very non-smooth maximum principle with state constraints , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[10]  David A. Anisi,et al.  Nearly time-optimal paths for a ground vehicle , 2003 .

[11]  Kevin M. Lynch,et al.  Controllability of a planar body with unilateral thrusters , 1999, IEEE Trans. Autom. Control..

[12]  Zexiang Li,et al.  A variational approach to optimal nonholonomic motion planning , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[13]  P. B. Coaker,et al.  Applied Dynamic Programming , 1964 .

[14]  W. Fulton,et al.  Lie Algebras and Lie Groups , 2004 .

[15]  J. Zabczyk Some comments on stabilizability , 1989 .

[16]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[17]  M. L. Chambers The Mathematical Theory of Optimal Processes , 1965 .

[18]  A. D. Lewis,et al.  Geometric Control of Mechanical Systems , 2004, IEEE Transactions on Automatic Control.

[19]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[20]  Michael E. Taylor,et al.  Differential Geometry I , 1994 .

[21]  Francesco Bullo,et al.  Series Expansions for the Evolution of Mechanical Control Systems , 2001, SIAM J. Control. Optim..

[22]  Jean-Paul Laumond,et al.  Controllability of a multibody mobile robot , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[23]  Gerardo Lafferriere,et al.  Motion planning for controllable systems without drift , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[24]  H. Sussmann,et al.  Underwater vehicles: the minimum time problem , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[25]  Eduardo Sontag Gradient techniques for systems with no drift: a classical idea revisited , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[26]  H. Sussmann,et al.  A continuation method for nonholonomic path-finding problems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[27]  C. M. Place Dynamical Systems: Differential Equations, Maps, and Chaotic Behaviour , 1992 .

[28]  L. Dubins On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents , 1957 .

[29]  Alonzo Kelly,et al.  Generating near minimal spanning control sets for constrained motion planning in discrete state spaces , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[30]  W. Boothby An introduction to differentiable manifolds and Riemannian geometry , 1975 .

[31]  R. Abgrall Numerical discretization of the first‐order Hamilton‐Jacobi equation on triangular meshes , 1996 .

[32]  Naomi Ehrich Leonard,et al.  Averaging for attitude control and motion planning , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[33]  L. Shepp,et al.  OPTIMAL PATHS FOR A CAR THAT GOES BOTH FORWARDS AND BACKWARDS , 1990 .

[34]  A. Bloch,et al.  Nonholonomic Control Systems on Riemannian Manifolds , 1995 .

[35]  P. Souéres,et al.  Shortest paths synthesis for a car-like robot , 1996, IEEE Trans. Autom. Control..

[36]  Devin J. Balkcom,et al.  Time Optimal Trajectories for Bounded Velocity Differential Drive Vehicles , 2002, Int. J. Robotics Res..

[37]  Thierry Fraichard,et al.  From Reeds and Shepp's to continuous-curvature paths , 1999, IEEE Transactions on Robotics.

[38]  Francesco Bullo,et al.  Series expansions for analytic systems linear in control , 2002, Autom..

[39]  Vladimir Borisov,et al.  Theory of Chattering Control , 1994 .

[40]  David L. Elliott,et al.  Geometric control theory , 2000, IEEE Trans. Autom. Control..

[41]  J. Klamka Controllability of dynamical systems , 1991, Mathematica Applicanda.

[42]  V. Arnold Mathematical Methods of Classical Mechanics , 1974 .

[43]  Thierry Fraichard,et al.  Collision-free and continuous-curvature path planning for car-like robots , 1997, Proceedings of International Conference on Robotics and Automation.

[44]  Devin J. Balkcom,et al.  Minimum Wheel-Rotation Paths for Differential-Drive Mobile Robots , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[45]  K. B. Haley,et al.  Optimization Theory with Applications , 1970 .

[46]  Frédéric Jean,et al.  Geometry of nonholonomic systems , 1998 .

[47]  R. Murray,et al.  Differential Flatness of Mechanical Control Systems: A Catalog of Prototype Systems , 1995 .

[48]  I. Michael Ross,et al.  Pseudospectral methods for optimal motion planning of differentially flat systems , 2004, IEEE Transactions on Automatic Control.

[49]  A. Borisov,et al.  On the History of the Development of the Nonholonomic Dynamics , 2005, nlin/0502040.

[50]  Daniel Feltey MATRIX GROUPS , 2008 .

[51]  R. Brockett Control Theory and Singular Riemannian Geometry , 1982 .

[52]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[53]  S. Zagatti On viscosity solutions of Hamilton-Jacobi equations , 2008 .

[54]  Jean-Paul Laumond,et al.  Topological property for collision-free nonholonomic motion planning: the case of sinusoidal inputs for chained form systems , 1998, IEEE Trans. Robotics Autom..

[55]  H. Sussmann A general theorem on local controllability , 1987 .

[56]  R. Bertram,et al.  Stochastic Systems , 2008, Control Theory for Physicists.

[57]  A. Divelbiss,et al.  Nonholonomic path planning with inequality constraints , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[58]  Alonzo Kelly,et al.  Reactive Nonholonomic Trajectory Generation via Parametric Optimal Control , 2003, Int. J. Robotics Res..

[59]  Warren E. Dixon,et al.  Nonlinear Control of Engineering Systems: A Lyapunov-Based Approach , 2003 .

[60]  Todd D. Murphey,et al.  Control of multiple model systems , 2002 .

[61]  Giuseppe Oriolo,et al.  Feedback control of a nonholonomic car-like robot , 1998 .

[62]  Nahum Shimkin,et al.  Nonlinear Control Systems , 2008 .

[63]  Jean-Paul Laumond,et al.  Guidelines in nonholonomic motion planning for mobile robots , 1998 .

[64]  Jean-Daniel Boissonnat,et al.  Shortest paths of bounded curvature in the plane , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[65]  Arjan van der Schaft,et al.  Non-linear dynamical control systems , 1990 .

[66]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[67]  S. Sastry Nonlinear Systems: Analysis, Stability, and Control , 1999 .

[68]  Leonid Gurvits,et al.  Averaging approach to nonholonomic motion planning , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[69]  P. Varaiya,et al.  Differential games , 1971 .

[70]  Ian M. Mitchell,et al.  Overapproximating Reachable Sets by Hamilton-Jacobi Projections , 2003, J. Sci. Comput..

[71]  Huibert Kwakernaak,et al.  Linear Optimal Control Systems , 1972 .

[72]  Carmen Chicone,et al.  Stability Theory of Ordinary Differential Equations , 2009, Encyclopedia of Complexity and Systems Science.

[73]  J. Sussmann,et al.  SHORTEST PATHS FOR THE REEDS-SHEPP CAR: A WORKED OUT EXAMPLE OF THE USE OF GEOMETRIC TECHNIQUES IN NONLINEAR OPTIMAL CONTROL. 1 , 1991 .

[74]  G. Swaminathan Robot Motion Planning , 2006 .

[75]  Robert F. Stengel,et al.  Optimal Control and Estimation , 1994 .

[76]  S. Sastry,et al.  Nonholonomic motion planning: steering using sinusoids , 1993, IEEE Trans. Autom. Control..

[77]  D. Normand-Cyrot,et al.  An introduction to motion planning under multirate digital control , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[78]  Philippe Souères,et al.  Optimal trajectories for nonholonomic mobile robots , 1998 .

[79]  Kevin M. Lynch,et al.  Kinematic controllability for decoupled trajectory planning in underactuated mechanical systems , 2001, IEEE Trans. Robotics Autom..

[80]  A. T. Fuller,et al.  Relay control systems optimized for various performance criteria , 1960 .

[81]  Sean R Eddy,et al.  What is dynamic programming? , 2004, Nature Biotechnology.