warm_start#

Initial trajectory generation for iLQR warm-starting.

namespace saltro
namespace optimizer

Functions

bool warm_start(const PlannerSettings &settings, const Satellite &satellite, const Satellite::VecX &x0, const Eigen::Ref<const Eigen::VectorXd> &jtime, const Eigen::Ref<const Eigen::MatrixXd> &q_goal, const Eigen::Ref<const Eigen::MatrixXd> &boresight, int N, const Eigen::Matrix<double, 3, saltro::limits::MAX_LENGTH_TRAJ> &R, const Eigen::Matrix<double, 3, saltro::limits::MAX_LENGTH_TRAJ> &V, const Eigen::Matrix<double, 3, saltro::limits::MAX_LENGTH_TRAJ> &B, const Eigen::Matrix<double, 3, saltro::limits::MAX_LENGTH_TRAJ> &S, const Eigen::Matrix<double, 1, saltro::limits::MAX_LENGTH_TRAJ> &rho, Eigen::Ref<Eigen::MatrixXd> X, Eigen::Ref<Eigen::MatrixXd> U)#

Generate initial trajectory for warm-starting iLQR optimization.

Produces a kinematically feasible initial guess for the state and control trajectories by simulating the satellite under a reference controller (e.g., B-dot, zero control, or excitation controller) specified in the settings.

The warm-start trajectory is computed by:

  1. Selecting the reference controller from settings.init_traj.initcontroller

  2. Forward-propagating the dynamics from x0 using the controller:

    \[ \mathbf{x}_{k+1} = \mathbf{f}(\mathbf{x}_k, \mathbf{u}_k^{\text{ref}}, t_k) \]
    where \(\mathbf{u}_k^{\text{ref}}\) is computed by the reference controller

  3. Storing the resulting state and control sequences in X and U

A good warm-start is crucial for iLQR convergence, as it:

  • Initializes the trajectory near the feasible constraint manifold

  • Reduces initial cost to reasonable values

  • Provides a starting point within the basin of attraction of the optimizer

Typical controllers used:

  • B-dot controller: Detumbles the satellite by opposing magnetic field rate

  • Zero controller: Open-loop propagation with zero actuation

  • Excitation controller: Adds persistent excitation for parameter estimation

Parameters:

  • settings – Planner settings containing initial trajectory configuration (controller type, gains, etc.)

  • satellite – Satellite model with dynamics and reference controllers

  • x0 – Initial attitude state (7+nRW × 1): [ω(3), q(4), h_rw(nRW)]

  • jtime – Mission time vector in Julian centuries (N × 1)

  • q_goal – Goal quaternion trajectory (4 × N) for reference controller

  • boresight – Boresight constraint trajectory (3 × N), unit vectors

  • N – Horizon length (number of timesteps)

  • R – Position trajectory in ECI frame (3 × MAX_LENGTH_TRAJ), meters

  • V – Velocity trajectory in ECI frame (3 × MAX_LENGTH_TRAJ), m/s

  • B – Magnetic field trajectory in ECI frame (3 × MAX_LENGTH_TRAJ), Tesla

  • S – Sun direction trajectory in ECI frame (3 × MAX_LENGTH_TRAJ), unit vectors

  • rho – Atmospheric density trajectory (1 × MAX_LENGTH_TRAJ), kg/m³

  • X – Output: initial state trajectory (N × state_dim)

  • U – Output: initial control trajectory (N-1 × input_dim)

Returns:

true if warm-start succeeded, false if propagation failed