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Sequential Convex Programming for 6-DoF Powered Descent Guidance with Continuous-Time Compound State-Triggered Constraints

Samet Uzun, Behcet Acikmese, John M. Carson

TL;DR

This paper presents a sequential convex programming framework for ensuring the continuous-time satisfaction of compound state-triggered constraints, a subset of logical specifications, in the powered descent guidance (PDG) problem, which combines the generalized mean-based smooth robustness measure (D-GMSR) with the continuous-time successive convexification method.

Abstract

This paper presents a sequential convex programming (SCP) framework for ensuring the continuous-time satisfaction of compound state-triggered constraints, a subset of logical specifications, in the powered descent guidance (PDG) problem. The proposed framework combines the generalized mean-based smooth robustness measure (D-GMSR), a parameterization technique tailored for expressing discrete-time temporal and logical specifications through smooth functions, with the continuous-time successive convexification (CT-SCvx) method, a real-time solution for constrained trajectory optimization that guarantees continuous-time constraint satisfaction and convergence. The smoothness of the temporal and logical specifications parameterized via D-GMSR enables solving the resulting optimization problem with robust and efficient SCP algorithms while preserving theoretical guarantees. In addition to their smoothness, the parameterized specifications are sound and complete, meaning the specification holds if and only if the constraint defined by the parameterized function is satisfied. The CT-SCvx framework is then applied to solve the parameterized problem, incorporating: (1) reformulation for continuous-time path constraint satisfaction, (2) time-dilation to transform the free-final-time PDG problem into a fixed-final-time problem, (3) multiple shooting for exact discretization, (4) exact penalty functions for penalizing nonconvex constraints, and (5) the prox-linear method, a convergence-guaranteed SCP algorithm, to solve the resulting finite-dimensional nonconvex PDG problem. The effectiveness of the framework is demonstrated through a numerical simulation. The implementation is available at https://github.com/UW-ACL/CT-cSTC

Sequential Convex Programming for 6-DoF Powered Descent Guidance with Continuous-Time Compound State-Triggered Constraints

TL;DR

This paper presents a sequential convex programming framework for ensuring the continuous-time satisfaction of compound state-triggered constraints, a subset of logical specifications, in the powered descent guidance (PDG) problem, which combines the generalized mean-based smooth robustness measure (D-GMSR) with the continuous-time successive convexification method.

Abstract

This paper presents a sequential convex programming (SCP) framework for ensuring the continuous-time satisfaction of compound state-triggered constraints, a subset of logical specifications, in the powered descent guidance (PDG) problem. The proposed framework combines the generalized mean-based smooth robustness measure (D-GMSR), a parameterization technique tailored for expressing discrete-time temporal and logical specifications through smooth functions, with the continuous-time successive convexification (CT-SCvx) method, a real-time solution for constrained trajectory optimization that guarantees continuous-time constraint satisfaction and convergence. The smoothness of the temporal and logical specifications parameterized via D-GMSR enables solving the resulting optimization problem with robust and efficient SCP algorithms while preserving theoretical guarantees. In addition to their smoothness, the parameterized specifications are sound and complete, meaning the specification holds if and only if the constraint defined by the parameterized function is satisfied. The CT-SCvx framework is then applied to solve the parameterized problem, incorporating: (1) reformulation for continuous-time path constraint satisfaction, (2) time-dilation to transform the free-final-time PDG problem into a fixed-final-time problem, (3) multiple shooting for exact discretization, (4) exact penalty functions for penalizing nonconvex constraints, and (5) the prox-linear method, a convergence-guaranteed SCP algorithm, to solve the resulting finite-dimensional nonconvex PDG problem. The effectiveness of the framework is demonstrated through a numerical simulation. The implementation is available at https://github.com/UW-ACL/CT-cSTC

Paper Structure

This paper contains 18 sections, 45 equations, 2 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. 6-DoF Powered Descent Guidance Problem with Continuous-time Compound State-Trigerred Constraints
  3. Rocket Dynamics:
  4. General state and control constraints
  5. Boundary conditions
  6. Compound state-triggered constraints
  7. Sequential Convex Programming based Solution Method
  8. Parametrization of Temporal and Logical Specifications
  9. STL syntax
  10. Generalized mean-based smooth robustness (D-GMSR)
  11. Continuous-time Successive Convexification Framework:
  12. Reformulation of the path constraints
  13. Time-dilation
  14. Parameterization of the control input and exact discretization of the dynamics
  15. Penalization of the nonconvex constraints
  16. ...and 3 more sections

Figures (2)

  • Figure 1: The landing trajectory of the rocket.
  • Figure 2: State and control inputs of the rocket during landing.

Theorems & Definitions (3)

  • Remark 1
  • Remark 2
  • Remark 3