A novel approach for optimal trajectory design with multiple operation modes of propulsion system, part 2

Abstract

Equipping a spacecraft with multiple solar-powered electric engines (of the same or different types) compounds the task of optimal trajectory design due to presence of both real-valued inputs (power input to each engine in addition to the direction of thrust vector) and discrete variables (number of active engines).Each engine can be switched on/off independently and "optimal" operating power of each engine depends on the available solar power, which depends on the distance from the Sun. Application of the Composite Smooth Control (CSC) framework to a heliocentric fuel-optimal trajectory optimization from the Earth to the comet 67P/Churyumov-Gerasimenko is demonstrated, which presents a new approach to deal with multiple-engine problems. Operation of engine clusters with 4, 6, 10 and even 20 engines of the same type can be optimized.Moreover, engine clusters with different/mixed electric engines are considered with either 2, 3 or 4 different types of engines. Remarkably, the CSC framework allows us 1) to reduce the original multi-point boundary-value problem to a two-point boundary-value problem (TPBVP), and 2) to solve the resulting TP-BVPs using a single-shooting solution scheme and with a random initialization of the missing costates. While the approach we present is a continuous neighbor of the discontinuous extremals, we show that the discontinuous necessary conditions are satisfied in the asymptotic limit. We believe this is the first indirect method to accommodate a multi-mode control of this level of complexity with realistic engine performance curves. The results are interesting and promising for dealing with a large family of such challenging multi-mode optimal control problems.

Trajectory Optimization with Complex Obstacle Avoidance Constraints via Homotopy Network Sequential Convex Programming

“…First, finite element software or CAD software was used to model the obstacle; the blue area represents the cavity, and the yellow area represents the obstacle. Then, the interface regression speed was set according to (24), and the boundary conditions were set according to (23). After dividing the uniform triangular second-order element or the tetrahedral second-order element, the Newton iteration method was used to solve (21) to obtain the T field.…”

“…The general idea of the homotopy technique is to solve a series of simple transition problems so that the solution of the transition problem gradually approaches the optimal solution of the primal problem. This method reduces the problem's difficulty, thereby significantly improving the success rate of trajectory planning [4,[23][24][25][26][27].…”

“…Taheri [23,24] and Saranathan [25] first used the homotopy method to convert a multipoint boundary value problem into an easier-to-solve two-point boundary value problem, thereby dealing with multiple propulsion modes and dynamic environments. Malyuta [26] combined the homotopy method with the SCP algorithm to solve trajectory planning in a rendezvous maneuver under the constraints of discrete logic.…”

A Novel Approach for Optimal Trajectory Design with Multiple Operation Modes of Propulsion System, Part 1

“…Motivated in part by the method of [46], we present here a new framework, called Composite Smooth Control (CSC), within the indirect optimization formalism to deal with the problem of interplanetary trajectory design. Specifically, we focus on problems in which the spacecraft is equipped either with 1) a variable-I sp , variable-thrust (VIVT) engine (in part 1 of this set of two papers) or 2) a cluster of engines (in part 2 [47]). However, we treat the problem by modifying the admissible control in the optimal control formulation and introduce an approach to smooth the otherwise discrete switches.…”

“…A prominent feature of the proposed framework is that not only the optimal instances of transition between different operation modes (in the case of a VIVT engine), but also the optimal number of engines (e.g., in the case of a cluster of engines) as well as their optimal operating conditions are revealed without a priori assumptions. The multi-engine problem is considered in part 2 [47].…”