Enhancements are incorporated to allow faster convergence to the fuel optimal solution.

An enhanced algorithm is developed that builds on a previous innovation of fuel-optimal powered-descent guidance (PDG) for planetary pinpoint landing. The PDG problem is to compute constrained, fuel-optimal trajectories to land a craft at a prescribed target on a planetary surface, starting from a “parachute cut-off” point and using a throttleable descent engine. The previous innovation showed the minimal-fuel PDG problem can be posed as a convex optimization problem, in particular, as a Second-Order Cone Program, which can be solved to global optimality with deterministic convergence properties, and hence is a candidate for onboard implementation. To increase the speed and robustness of this convex PDG algorithm for possible onboard implementation, the following enhancements are incorporated:

  • Fast detection of infeasibility (i.e., control authority is not sufficient for softlanding) for subsequent fault response.
  • The use of a piecewise-linear control parameterization, providing smooth solution trajectories and increasing computational efficiency.
  • An enhanced line-search algorithm for optimal time-of-flight, providing quicker convergence and bounding the number of path-planning iterations needed.
  • An additional constraint that analytically guarantees inter-sample satisfaction of glide-slope and non-sub-surface flight constraints, allowing larger discretizations and, hence, faster optimization.
  • Explicit incorporation of Mars rotation rate into the trajectory computation for improved targeting accuracy.

These enhancements allow faster convergence to the fuel-optimal solution and, more importantly, remove the need for a “human-in-the-loop,” as constraints will be satisfied over the entire path-planning interval independent of step-size (as opposed to just at the discrete time points) and infeasible initial conditions are immediately detected. Finally, while the PDG stage is typically only a few minutes, ignoring the rotation rate of Mars can introduce 10s of meters of error.

By incorporating it, the enhanced PDG algorithm becomes capable of pinpoint targeting.

This work was done by Behcet Acikmese, James C. Blackmore, and Daniel P. Scharf of Caltech for NASA’s Jet Propulsion Laboratory. For more information, contact This email address is being protected from spambots. You need JavaScript enabled to view it..

In accordance with Public Law 96-517, the contractor has elected to retain title to this invention. Inquiries concerning rights for its commercial use should be addressed to:

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Refer to NPO-46648, volume and number of this NASA Tech Briefs issue, and the page number.

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