This is a Python Gym environment to simulate a 6 degrees of freedom rocket.

• full 6DOF rocket landing environment
• realistic dynamics equation modeled on a rigid body assumption
• interactive 3D visualization through PyVista
• actuators available:
  1. thruster
  2. fins
• Wandb logging wrapper

The environment employes a continuous action space, with the engine allowed to throttle between maxThrust and minThrust. The thrust was normalized to lie in the range [-1, +1] as best practice for convergence of the algorithms suggest. The engine is gimbaled by two angles $\delta_y$ and $\delta_z$ around two hinge points, respectively moving the engine around the z and y axis.

Research question:

• Is there a reduction in fuel consumption when the thruster is aided by fins? Quantify it.

• Pitch plane ( x - z ) corresponding to i={1,2}:

  • Diagram of the angles

  • Position vector of the fin i in body coordinates:

    $$ \vec{x}^{B,i} = \begin{bmatrix} x_{fin}^i \ \pm r_{base} \ 0 \end{bmatrix} $$

• Yaw plane ( x - y ) corresponding to i={3,4}:

  • Diagram of the angles

  • Position vector of the fin i in body coordinates: $$\vec{x}^{B,i} = \begin{bmatrix}x_{fin}^i \ 0 \ \pm r_{base}\end{bmatrix}$$

To compute the force generated by the fin i in body axis we have to:

1. Neglecting wind, we can compute the air velocity of the center of mass of the vehicle as:

   $$ \vec{v}^B_{air} = R_{I \rightarrow B}\vec{v}^I$$

2. Compute the velocity vector at each fin location i (denoted by its position vector in body coordinates $\vec{x}^{B,i}$), taking into account the rotation of the rocket:

   $$ \vec{v}^{B,i}{air} = \vec{v}^B{air} + \vec{\omega}^B \times \left[ \vec{x}^{B,i} - \vec{x}^{B,CG}\right] $$

3. Compute the aerodynamic angles at the location of each fin i:

   • x-z plane aerodynamic angle:

     $$\alpha^i = \arctan 2 \left[ \frac{v_z^{B,i}}{v_x^{B,i}} \right]$$

   • x-y plane aerodynamic angle:

     $$ \beta^i = \arcsin \left[ \frac{v_y^{B,i}}{||\vec{v}^{B,i}||} \right] $$

4. Input the angle of deflection from the longitudinal axis of the fin $\beta_{fin,i}$ (i.e. the control input).

5. Compute the angle of attack $AoA$ of each fin i:

   • Yaw plane ( x - y ): $$AoA_i = -\beta_{fin,i} - \beta^i$$

   • Pitch plane ( x - z ): $$AoA_i = \beta_{fin,i} - \alpha^i$$

6. Compute the aerodynamic pressure $$q=\frac{1}{2}\rho(x)||\vec{\vec{v}^{B,i}_{air}}||$$

7. Compute the normal force coefficient $C_f$:

   $$ C_f(AoA_i)=\bar{C_f} \sin{AoA_i} $$

8. Compute the aerodynamic force at each fin i:

   • Yaw plane ( x - y ):

     $$ \vec{F}^B_{fin,i} = qS_{fin}C_f\left(AoA_i\right) \begin{bmatrix} \sin{\beta_{fin,i}} & \cos{\beta_{fin,i}} & 0 \end{bmatrix}^T$$

   • Pitch plane ( x - z ):

     $$ \vec{F}^B_{fin,i} = qS_{fin}C_f\left(AoA_i\right) \begin{bmatrix} -\sin{\beta_{fin,i}} & 0 & \cos{\beta_{fin,i}} \end{bmatrix}^T$$

9. Compute the aerodynamic torque for each fin i:

   $$ M^i = \left[ \vec{x}^{B,i} - \vec{x}^{B,CG}\right] \times \vec{F}^B_{fin,i} $$