Lorenzo A. Ricciardi

Multi-objective optimal control of ascent trajectories for launch vehicles

This paper presents a novel approach to the solution of multi-objective optimal control problems. The proposed solution strategy is based on the integration of the Direct Finite Elements Transcription method, to transcribe dynamics and objectives, with a memetic strategy called Multi Agent Collaborative Search (MACS). The original multi-objective optimal control problem is reformulated as a bi-level nonlinear programming problem. In the outer level, handled by MACS, trial control vectors are generated and passed to the inner level, which enforces the solution feasibility. Solutions are then returned to the outer level to evaluate the feasibility of the corresponding objective functions, adding a penalty value in the case of infeasibility. An optional single level refinement is added to improve the ability of the scheme to converge to the Pareto front. The capabilities of the proposed approach will be demonstrated on the multi-objective optimisation of ascent trajectories of launch vehicles.

Vehicle and mission design of a future small payload launcher

This paper presents the conceptual design and performance analysis of a partially reusable space launch vehicle for small payloads. The system uses a multi-stage vehicle with rocket engines, with a reusable first stage capable of glided or powered flight, and expendable upper stage(s) to inject a 500 kg payload in different low Earth orbits. The space access vehicle is designed to be air-launched from a modified aircraft carrier. The aim of the system design is to develop a commercially viable launch system for near-term operation, thus emphasis is placed on the efficient use of high TRL technologies. The vehicle design are analysed using a multi-disciplinary design optimisation approach to evaluate the performance, operational capabilities and design trade-offs.

A direct memetic approach to the solution of Multi-Objective Optimal Control Problems

This paper proposes a memetic direct transcription algorithm to solve Multi-Objective Optimal Control Problems (MOOCP). The MOOCP is first transcribed into a Non-linear Programming Problem (NLP) with Direct Finite Elements in Time (DFET) and then solved with a particular formulation of the Multi Agent Collaborative Search (MACS) framework. Multi Agent Collaborative Search is a memetic algorithm in which a population of agents combines local search heuristics, exploring the neighbourhood of each agent, with social actions exchanging information among agents. A collection of all Pareto optimal solutions is maintained in an archive that evolves towards the Pareto set. In the approach proposed in this paper, individualistic actions run a local search, from random points within the neighbourhood of each agent, solving a normalised Pascoletti-Serafini scalarisation of the multi-objective NLP problem. Social actions, instead, solve a bi-level problem in which the lower level handles only the constraint equations while the upper level handles only the objective functions. The proposed approach is tested on the multi-objective extensions of two well-known optimal control problems: the Goddard Rocket problem, and the maximum energy orbit rise problem.

Global solution of multi-objective optimal control problems with multi agent collaborative search and direct finite elements transcription

This paper addresses the solution of optimal control problems with multiple and possibly conflicting objective functions. The solution strategy is based on the integration of Direct Finite Elements in Time (DFET) transcription into the Multi Agent Collaborative Search (MACS) framework. Multi Agent Collaborative Search is a memetic algorithm in which a population of agents performs a set of individual and social actions looking for the Pareto front. Direct Finite Elements in Time transcribe an optimal control problem into a constrained Non-linear Programming Problem (NLP) by collocating states and controls on spectral bases. MACS operates directly on the NLP problem and generates nearly-feasible trial solutions which are then submitted to a NLP solver. If the NLP solver converges to a feasible solution, an updated solution for the control parameters is returned to MACS, along with the corresponding value of the objective functions. Both the updated guess and the objective function values will be used by MACS to generate new trial solutions and converge, as uniformly as possible, to the Pareto front. To demonstrate the applicability of this strategy, the paper presents the solution of the multi-objective extensions of two well-known space related optimal control problems: the Goddard Rocket problem, and the maximum energy orbit rise problem.

Improved Archiving and Search Strategies for Multi Agent Collaborative Search

This paper presents a new archiving strategy and some modified search heuristics for the Multi Agent Collaborative Search algorithm (MACS). MACS is a memetic scheme for multi-objective optimisation that combines the local exploration of the neighbourhood of some virtual agents with social actions to advance towards the Pareto front. The new archiving strategy is based on the physical concept of minimising the potential energy of a cloud of points each of which repels the others. Social actions have been modified to better exploit the information in the archive and local actions dynamically adapt the maximum number of coordinates explored in the pattern search heuristic. The impact of these modifications is tested on a standard benchmark and the results are compared against MOEA/D and a previous version of MACS. Finally, a real space related problem is tackled.

Multi-objective optimal control of re-entry and abort scenarios

This paper presents a novel approach to the solution of multi-phase multi-objective optimal control problems. The proposed solution strategy is based on the integration of the Direct Finite Elements Transcription (DFET) method, to transcribe dynamics and objectives, with a memetic strategy called Multi Agent Collaborative Search (MACS). The original multi-objective optimal control problem is reformulated as two non-linear programming problems: a bi-level and a single level one. In the bi-level problem the outer level, handled byMACS, generates trial control vectors that are then passed to the inner level, which enforces the feasibility of the solution. Feasible control vectors are then returned to the outer level to evaluate the corresponding objective functions. A single level refinement is then run to improve local convergence to the Pareto front. The paper introduces also a novel parameterisation of the controls, using Bernstein polynomials, in the context of the DFET transcription method. The approach is first tested on a known atmospheric re-entry problem and then applied to the analysis of ascent and abort trajectories for a space plane.

Multi Agent Collaborative Search

This chapter presents an overview of Multi Agent Collaborative Search (MACS), for multi-objective optimisation with an analysis of different heuristics for local search. In particular the effects of simple inertia and differential evolution operators in combination with pattern search and gradient methods are investigated. Different benchmarks are used to demonstrate the effectiveness of the MACS framework and of the heuristics for both local and global search. The MACS framework is tested on two sets of academic problems and two real space mission design problems using the IGD and the success rate as performance metrics. The performance of MACS is compared against three known multi-objective optimisation algorithms: NSGA-II, MOAED and MTS.

Multi-objective optimisation of constellation deployment using low-thrust propulsion

This work presents an analysis of the deployment of future constellations using a com-bination of low-thrust propulsion and natural dynamics. Different strategies to realise the transfer from the launcher injection orbit to the constellation operational orbit are investigated. The deployment of the constellation is formulated as a multi-objective optimisation problem that aims at minimising the maximum transfer ΔV, the launch cost and maximise at the same time the pay-off given by the service provided by the constellation. The paperwill consider the case of a typical constellation with 27 satellites in Medium Earth Orbit and the use of only two launchers, one of which can carry a single satellite. It will be demonstrated that some strategies and deployment sequences are dominant and provide the best trade-off between peak transfer ΔV and monetary pay-off.