Loss of stability of guidance and control laws for autonomous vehicles

The problem of dynamic loss of stability of straight-line motion of a heading autopilot coupled with pursuit or proportional navigation guidance laws for an autonomous underwatervehicle is considered. The controller and navigator gain selections and the navigator lookahead distance serve as the main bifurcation parameters. Hopf-bifurcation-theory techniques are used in order to establish stability of the resulting periodic solutions after the initial loss of stability of straight-line motion. Numerical integrations support the analytical predictions. Compari- sons between different guidance schemes are made and guidelines for safer and more accurate vehicle operations are provided.

[1]  Jean-Jacques E. Slotine,et al.  Robust trajectory control of underwater vehicles , 1985 .

[2]  Y. Kanayama,et al.  Smooth Local Path Planning for Autonomous Vehicles , 1990, Autonomous Robot Vehicles.

[3]  Robert B. McGhee,et al.  A simulation study of an autonomous steering system for on-road operation of automotive vehicles / Robert B. McGhee, Michael J. Zyda, Chiam Huat Tan , 1986 .

[4]  J. Carr.  Applications of Centre Manifold Theory , 1981 .

[5]  Fotis A. Papoulias.  BIFURCATION ANALYSIS OF LINE OF SIGHT VEHICLE GUIDANCE USING SLIDING MODES , 1991 .

[6]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[7]  B. Hassard,et al.  Bifurcation formulae derived from center manifold theory , 1978 .

[8]  Philip Holmes,et al.  Center manifolds, normal forms and bifurcations of vector fields with application to coupling between periodic and steady motions ☆ , 1981 .

[9]  R. McGhee,et al.  Optimal biased proportional navigation , 1968 .

[10]  H. B. Stewart,et al.  Towards a classification of generic bifurcations in dissipative dynamical systems , 1986 .

[11]  Y. Ho,et al.  Differential games and optimal pursuit-evasion strategies , 1965 .

[12]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[13]  A. J. Healey,et al.  Adaptive sliding mode control of autonomous underwater vehicles in the dive plane , 1990 .

[14]  M. Golubitsky,et al.  Singularities and groups in bifurcation theory , 1985 .