Nonlinear Trajectory Generation for Autonomous Vehicles via Parametrized Maneuver Classes

Abstract

A technique is presented for creating continuously parameterized classes of feasible system trajectories. These classes, which are useful for higher-level vehicle motion planners, follow directly from a small collection of userprovided example motions. A dynamically feasible trajectory interpolation algorithm generates a continuous family of vehicle maneuvers across a range of boundary conditions while enforcing nonlinear system equations of motion as well as nonlinear equality and inequality constraints. The scheme is particularly useful for describing motions that deviate widely from the range of linearized dynamics and where satisfactory example motions may be found from off-line nonlinear programming solutions or motion capture of human-piloted flight. The interpolation algorithm is computationally efficient, making it a viable method for real-time maneuver synthesis, particularly when used in concert with a vehicle motion planner. Experimental application to a three-degree-of-freedom rotorcraft test bed demonstrates the essential features of system and trajectory modeling, maneuver example selection, maneuver class synthesis, and integration into a hybrid system path planner. Nomenclature= goal-attainment binary variable b man = maneuver class binary variable C c, j = time duration constant for maneuver class j C s, j = time duration matrix for maneuver class j c i = vehicle model coefficientsmaneuver class duration state D x = differentiation operator with respect to variable x d i = vehicle model coefficients e = data matching error metric F = nonlinear equation set f = nonlinear program objective functioñ f = continuous-time dynamic consistency function g = inequality constraint vector H = planning decision horizon . ¶ Principal Member, Technical Staff, 555 Technology Square; mcconley@draper.com. h = equality constraint vector h bc = boundary condition equality constraint vector h 0 bc = boundary condition equality constraints invariant with α h em = dynamic consistency equality constraint vector h em = continuous-time dynamic consistency function i = summation index J = planning objective function J i = active constraint set i j = summation index k = spline order; planning decision step k i = affine maneuver design constants for planning l = summation index = linear constraint M c, j = state transition vector for maneuver class j M s, j = state transition matrix for maneuver class j M = vector of large numbers m j = binary variable for maneuver class j N = number of data samples N f = number of final condition maneuver parameters N i = number of initial condition maneuver parameters n v = number of spline coefficients for signal v p = finite-dimensional trajectory parametrization S e = sampling of unit interval for equality constraints S g = sampling of unit interval for inequality constraints s = arc length in v-space s i = ith sampling point T = maneuver duration T s = linear-time invariant (LTI)-mode discretization interval t = time u = direct difference vector u = projected feasible difference vector...

Optimal Control Using Nonholonomic Integrators

“…A related approach, applied to an underwater eel-like robot, involves finding approximate solutions using truncated basis of cyclic input functions [4]. Other applications of symmetry in robotics include motion planning of dynamic variable inertia mechanical systems [5], improving the precision and efficiency of randomized kinodynamic planning [6], efficient motion planning using maneuver primitives [7], [8].…”

Three-dimensional path planning for unmanned aerial vehicle based on interfered fluid dynamical system

“…Using the optimal control theory to solve path planning problem can easily transform various constraints and optimal index into mathematical expressions but the solution demands large computation. Although the application of some new solutions such as pseudospectral method 12 and nonlinear trajectory generation 13 can share the computation burden, for complex terrain constraints, the 3D path planning problem is still complex with this method. Nikolos et al 14 used B-spline curves to simulate the 3D flight trajectory of aircraft, and then used an evolutionary algorithm to optimize the B-spline curve control points.…”

A Discrete Geometric Optimal Control Framework for Systems with Symmetries

“…Nevertheless, as already pointed out by several similar works cited in our references, this approach should be used to produce small-scale local solutions that are combined by more global methods in a hierarchical fashion (e.g. see [8] regarding incremental and roadmap planners, as well as [27,28] for planning using primitives). An obvious application is also the refinement of trajectories produced by discrete or sampling-based planners.…”