Forward Pass and Backward Sweep

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

The two core computational steps of DDP algorithms. The forward pass propagates from the initial state through the equations of motion at each stage using the current control sequence, producing the nominal state trajectory and evaluating the cost. The backward sweep recurses from the final stage backward, using gradient and Hessian information of the cost and constraints to solve for optimal control updates δu and parameter updates δw at each stage. One forward-backward pair constitutes a single iteration, repeated until optimality conditions are met.

Application Value

This concept is fundamental to cislunar orbital mechanics and mission analysis, providing essential theoretical support for trajectory design and operational planning.

  • Retrograde Motion
  • Absolute Phase Bias
  • Relative Attitude Quaternion
  • Radial-Tangential-Normal Coordinate System, RTN

References

  • Mayne 1966; Lantoine & Russell 2012, JOTA; Aziz et al. 2019, JGCD
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Contributors: ouyangjiahong, Ou Yang Jiahong