Adaptive Descent Controller

Overview:

The Adaptive Descent Controller implements an energy-guided landing strategy for a planetary or lunar lander.
Its objective is to safely guide the spacecraft from an initial descent state to a soft touchdown while respecting actuator limits and physical constraints.

The controller dynamically adjusts:
- target descent velocity
- controller gains
- descent mode

based on the brake ratio, which compares the remaining altitude to the required braking distance. The final thrust command is generated using a PD velocity controller combined with gravity compensation.
Both the controller and the regulator are derived from a virtual base class, enabling modular interchangeability of the respective models at runtime (see architecture).

System Inputs and Outputs

Inputs

The controller requires the following physical parameters:

Symbol	Description
$v$	Current vertical velocity
$h$	Current altitude
$m$	Current spacecraft mass
$g$	Local gravitational acceleration
$T_{max}$	Maximum available thrust
$dt$	Simulation timestep

Output

The controller produces:

T_{cmd}

which represents the thrust command in Newtons for the next timestep.

Maximum Achievable Acceleration

The maximum upward acceleration available to the lander is determined by the thrust-to-weight ratio.

a_{max} = \dfrac{T_{max}}{m} - g

To avoid numerical issues the implementation ensures

a_{max} \geq \epsilon

where $\epsilon$ is a small constant.

Braking Distance

The controller estimates the minimum distance required to stop the current descent velocity using basic kinematics.

d_{brake} = \dfrac{v^2}{2 \cdot a_{max}}

Brake Ratio

The brake ratio determines how much altitude remains relative to the required stopping distance.

R_{brake} = \dfrac{h}{d_{brake}}

Interpretation:

Symbol	Description
$R_{brake} >> 1$	Plenty of altitude available
$R_{brake} \approx 1$	Braking must start
$R_{brake} < 1$	Critical braking required

This parameter drives both:
- descent mode selection
- controller gain scheduling

Target Descent Velocity

The desired descent velocity is computed using an energy-based guidance law.

v_{target} = - \sqrt{2 \cdot k_r \cdot a_{max} \cdot h}

where the reserve factor $k_r$ provides an additional safety margin.
The negative sign ensures downward motion.

PD Velocity Controller

The controller attempts to track the target velocity using a Proportional-Derivative (PD) controller.

Control Error

e = v_{target} - v

Derivative Term

\dot{e} = \dfrac{e - e_{old}}{dt}

Control Acceleration

a_{ctrl} = K_p \cdot e + K_d \cdot \dot{e}

where
- $K_p$ = proportional gain
- $K_d$ = derivative gain
These gains are adaptively interpolated based on the brake ratio.

Gravity Compensation

To maintain stable descent, the controller adds a hover thrust component that compensates gravity.

T_{hover} = m \cdot g

Total Thrust Command

The final thrust command combines gravity compensation and the control acceleration.

T_{cmd} = T_{hover} + m \cdot a_{ctrl}

Thrust Saturation

The commanded thrust is limited to the physically available actuator range.

T_{cmd} = min(max(T_{cmd}, 0), T_{max})

Normalized Throttle Output

For actuator interfaces expecting a normalized throttle command:

u = \dfrac{T_{cmd}}{T_{max}}

0 \leq u \leq 1

Descent Modes

The descent controller operates in four phases determined by the brake ratio.

Mode	Condition	Description
MODE_A	$R_{brake} > 3$	Energy Dissipation
MODE_B	$1.5 < R_{brake} \leq 3$	Controlled Descent
MODE_C	$R_{brake} < 1$	Terminal Approach
MODE_D	otherwise	Critical Braking

Descent Phase Diagram

The diagram in Figure 1 visualizes the relationship between altitude $h$ and descent velocity $|v|$ during the landing phase.

h = \dfrac{v^2}{2a_{max}}

This curve represents the minimum altitude required to decelerate the spacecraft to zero velocity when applying maximum thrust.

Descent phase diagram — **Figure 1 — Safe Descent Corridor.**

The figure below illustrates how the controller switches between descent modes depending on the brake ratio during the landing trajectory.

Descent modes diagram — **Figure 2 — Descent Mode Selection.**

Characteristics of the Controller

Advantages

Energy-based descent planning
Adaptive gain scheduling
Gravity compensation
Actuator saturation handling

The controller therefore provides stable, safe and efficient landing behaviour across different phases of the descent trajectory.