Fuel-Efficient Powered Descent Guidance on Large Planetary Bodies via Theory of Functional Connections

Hunter Johnston, Enrico Schiassi, Roberto Furfaro, Daniele Mortari

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


In this paper we present a new approach to solve the fuel-efficient powered descent guidance problem on large planetary bodies with no atmosphere (e.g., Moon or Mars) using the recently developed Theory of Functional Connections. The problem is formulated using the indirect method which casts the optimal guidance problem as a system of nonlinear two-point boundary value problems. Using the Theory of Functional Connections, the problem’s linear constraints are analytically embedded into a functional, which maintains a free-function that is expanded using orthogonal polynomials with unknown coefficients. The constraints are always analytically satisfied regardless of the values of the unknown coefficients (e.g., the coefficients of the free-function) which converts the two-point boundary value problem into an unconstrained optimization problem. This process reduces the whole solution space into the admissible solution subspace satisfying the constraints and, therefore, simpler, more accurate, and faster numerical techniques can be used to solve it. In this paper a nonlinear least-squares method is used. In addition to the derivation of this technique, the method is validated in two scenarios and the results are compared to those obtained by the general purpose optimal control software, GPOPS-II. In general, the proposed technique produces solutions of O(1 0 − 10) accuracy. Additionally, for the proposed test cases, it is reported that each individual TFC-based inner-loop iteration converges within 6 iterations, each iteration exhibiting a computational time between 72 and 81 milliseconds, with a total execution time of 2.1 to 2.6 seconds using MATLAB. Consequently, the proposed methodology is potentially suitable for real-time computation of optimal trajectories.

Original languageEnglish (US)
Pages (from-to)1521-1552
Number of pages32
JournalJournal of the Astronautical Sciences
Issue number4
StatePublished - Dec 2020


  • Constraint embedding
  • Fuel optimal pinpoint landing
  • Indirect method
  • Least-squares
  • Optimal control
  • Theory of functional connections

ASJC Scopus subject areas

  • Aerospace Engineering
  • Space and Planetary Science


Dive into the research topics of 'Fuel-Efficient Powered Descent Guidance on Large Planetary Bodies via Theory of Functional Connections'. Together they form a unique fingerprint.

Cite this