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Robust Fuel-Optimal Landing Guidance for Hazardous Terrain using Multiple Sliding Surfaces

Sheikh Zeeshan Basar, Satadal Ghosh

TL;DR

The paper tackles the challenge of achieving hazard-avoided, fuel-efficient, precision soft landing in the presence of disturbances by extending the optimal terrain avoidance guidance law (OTALG) with multiple sliding surfaces. The proposed MSS-OTALG combines a ZEM/ZEV-based near-fuel-optimal core with two sliding surfaces and a state/time-dependent sliding parameter to enforce robust convergence while enabling terrain-divert maneuvers. It proves practical fixed-time stability and validates performance through extensive simulations, showing robust terrain avoidance, improved landing precision, and competitive fuel usage relative to existing methods. The work offers a principled, robust framework for safe planetary landings near hazardous terrain, with potential for online terrain adaptation through onboard perception.

Abstract

In any spacecraft landing mission, fuel-efficient precision soft landing while avoiding nearby hazardous terrain is of utmost importance. Very few existing literature have attempted addressing both the problems of precision soft landing and terrain avoidance simultaneously. To this end, an optimal terrain avoidance landing guidance (OTALG) was recently developed, which showed promising performance in avoiding the terrain while consuming near-minimum fuel. However, its performance significantly degrades in the face of external disturbances, indicating lack of robustness. To mitigate this problem, in this paper, a near fuel-optimal guidance law is developed to avoid terrain and achieve precision soft landing at the desired landing site. Expanding the OTALG formulation using sliding mode control with multiple sliding surfaces (MSS), the presented guidance law, named `MSS-OTALG', improves precision soft landing accuracy. Further, the sliding parameter is designed to allow the lander to avoid terrain by leaving the trajectory enforced by the sliding mode and eventually returning to it when the terrain avoidance phase is completed. And finally, the robustness of the MSS-OTALG is established by proving practical fixed-time stability. Extensive numerical simulations are also presented to showcase its performance in terms of terrain avoidance, low fuel consumption, and accuracy of precision soft landing under bounded atmospheric perturbations, thrust deviations, and constraints. Comparative studies against existing relevant literature validate a balanced trade-off of all these performance measures achieved by the developed MSS-OTALG.

Robust Fuel-Optimal Landing Guidance for Hazardous Terrain using Multiple Sliding Surfaces

TL;DR

The paper tackles the challenge of achieving hazard-avoided, fuel-efficient, precision soft landing in the presence of disturbances by extending the optimal terrain avoidance guidance law (OTALG) with multiple sliding surfaces. The proposed MSS-OTALG combines a ZEM/ZEV-based near-fuel-optimal core with two sliding surfaces and a state/time-dependent sliding parameter to enforce robust convergence while enabling terrain-divert maneuvers. It proves practical fixed-time stability and validates performance through extensive simulations, showing robust terrain avoidance, improved landing precision, and competitive fuel usage relative to existing methods. The work offers a principled, robust framework for safe planetary landings near hazardous terrain, with potential for online terrain adaptation through onboard perception.

Abstract

In any spacecraft landing mission, fuel-efficient precision soft landing while avoiding nearby hazardous terrain is of utmost importance. Very few existing literature have attempted addressing both the problems of precision soft landing and terrain avoidance simultaneously. To this end, an optimal terrain avoidance landing guidance (OTALG) was recently developed, which showed promising performance in avoiding the terrain while consuming near-minimum fuel. However, its performance significantly degrades in the face of external disturbances, indicating lack of robustness. To mitigate this problem, in this paper, a near fuel-optimal guidance law is developed to avoid terrain and achieve precision soft landing at the desired landing site. Expanding the OTALG formulation using sliding mode control with multiple sliding surfaces (MSS), the presented guidance law, named `MSS-OTALG', improves precision soft landing accuracy. Further, the sliding parameter is designed to allow the lander to avoid terrain by leaving the trajectory enforced by the sliding mode and eventually returning to it when the terrain avoidance phase is completed. And finally, the robustness of the MSS-OTALG is established by proving practical fixed-time stability. Extensive numerical simulations are also presented to showcase its performance in terms of terrain avoidance, low fuel consumption, and accuracy of precision soft landing under bounded atmospheric perturbations, thrust deviations, and constraints. Comparative studies against existing relevant literature validate a balanced trade-off of all these performance measures achieved by the developed MSS-OTALG.
Paper Structure (16 sections, 6 theorems, 36 equations, 8 figures, 3 tables)

This paper contains 16 sections, 6 theorems, 36 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. BACKGROUND AND PRELIMINARIES
  3. Dynamics and Preliminary Results
  4. Optimal Terrain Avoidance Guidance Law
  5. ROBUST OTALG USING MULTIPLE SLIDING SURFACES (MSS)
  6. MSS Design: Surface 1
  7. MSS Design: Surface 2
  8. ON THE CHOICE OF SLIDING PARAMETER
  9. SIMULATIONS AND DISCUSSIONS
  10. Simulation Setup and Parameters
  11. Illustration of a Numerical Example
  12. Comparative Simulation Study
  13. Comparison study under zero atmospheric perturbations
  14. Comparison study under non-zero atmospheric perturbations
  15. CONCLUSION
  16. ...and 1 more sections

Key Result

Theorem 3.1

The virtual controller defined by $\Dot{\mathbf{s}}_1 = -\frac{\Lambda}{t_{\mathrm{go}}}\mathbf{s}_1$, is globally stable. Further, both $\mathbf{s}_1$ and its derivative, under the reaching law defined by the virtual controller reach zero in finite time.

Figures (8)

  • Figure 1: Spacecraft Landing Geometry
  • Figure 2: Illustration of terrain and barrier around $n$-step shaped polygons. (basar2023fueloptimal)
  • Figure 3: Behaviour of $p_i$ with respect to $d_i$ for $l_{1,i} = 1,\,l_{2,i}=9500,\,l_{3,i}=500$.
  • Figure 4: Trajectory, velocity, commanded acceleration, divert term and sliding variables. [A: Divert manoeuvre 1 begins, B: Divert manoeuvre 1 ends, C: Divert manoeuvre 2 begins, D: Divert manoeuvre 2 ends]
  • Figure 5: Comparison of MSS-OTALG, aug. OSG and OTALG under no atmospheric perturbations.
  • ...and 3 more figures

Theorems & Definitions (12)

  • Theorem 3.1
  • proof
  • Theorem 3.2
  • proof
  • Definition 1: Duration of dominant divert manoeuvres
  • Remark 1
  • Proposition 1
  • proof
  • Theorem 4.1
  • proof
  • ...and 2 more