Rotorcraft Trajectory Optimization with Realizability Considerations

Energy Efficient Arrival with RTA Constraint for Urban eVTOL Operations

“…For example, differential thrust between opposite motors provides roll and pitch moments. 16 Previously, researchers [17][18][19] have successfully decoupled longitudinal and lateral dynamics for helicopters with the conventional design. In general, quadrotors have a more symmetrical design (the location of rotors and the axis of rotation w.r.t center of gravity) than the conventional helicopters.…”

“…Hence, to simplify the optimal control problem and reduce the computational time, the longitudinal dynamics of the eVTOL air taxi has been decoupled from lateral dynamics. [17][18][19] This allows us to solve the vertical trajectory generation problem as 2D flight dynamics problem in the vertical plane. The two-dimensional longitudinal dynamics model of the vehicle in a fixed inertial frame of reference is as follows:…”

Nonlinear Optimal Control Analysis of Helicopter Maneuver Problems Using the Indirect Method

“…On the other hand, dynamic optimization [6][7][8] computes the controls, the state, and possibly the final time that minimize a cost function, subject to state equations and to various other constraints, as required by the problem at hand. There are basically two alternative strategies for the numerical solution of a dynamic optimization problem.…”

“…The result becomes a nonlinear programming problem which can be solved by one of the efficient NLP (non-linear programming) methods. 7) An algorithm for dynamic optimization should be carefully selected by investigating various factors affecting convergence speed, convergence radius, flexibility, complexity, required computer storage, and accuracy, etc. 4,7) The direct method is the usual choice in application to helicopter flight dynamics because of its ease in handling state inequality constraints and its large convergence radius, which means a converged optimal solution can be obtained from a large range of different initial guesses.…”

“…Then the problem is reduced to a TPBVP (twopoint boundary value problem) in the infinite dimension and a suitable MSM (multiple-shooting method) can be used to resolve it in the finite dimension. [8][9][10] The second is the direct method, 6,7) which uses the discretized or parameterized equation for state equations, constraint equations and a cost function in the finite dimension. The result becomes a nonlinear programming problem which can be solved by one of the efficient NLP (non-linear programming) methods.…”