Feedback Linearization

Definition

Feedback linearization is a model-based control technique that cancels a system’s known nonlinear dynamics by inverting them in the control law, leaving a linear closed loop on which simpler (e.g. PD) compensators act. In dambrosio2024redundant it is the inner controller for a free-flying (fully-actuated 6-DOF base) chaser with a 7-DOF arm: the full coupled inertia and convective terms are inverted, and two PD loops — one on the base, one on the manipulator — drive the linearized error. (The source writes the inertia matrix $H$; the wiki’s canonical symbol is $M$.)

Key Equations

Coupled equation of motion (canonical inertia $M$, convective/Coriolis $C$):
$M(q)\ddot{q}+C(q,\dot{q})\dot{q}=\tau ,q=[q_0,q_m{]}^{\top }(\text{6-DOF base}+N\text{-DOF arm}).$
Model-based feedback-linearization control law with base/arm PD loops:
$\tau =\left\{\begin{array}{c}{\tau }_0\\ {\tau }_m\end{array}\right\}=M\left\{\begin{array}{c}\mathrm{PD}(q_0^{\ast }-q_0)\\ \mathrm{PD}(q_m^{\ast }-q_m)\end{array}\right\}+C\dot{q},$
gloss: pre-multiplying the PD command by $M$ and adding back $C\dot{q}$ cancels the plant, so each subsystem tracks a decoupled linear error (base held at the synchronized state; arm follows the guidance policy).

Source Support

• dambrosio2024redundant — the explicit free-flying multibody EoM (Eq. 1) and the model-based feedback-linearization control law with separate base and manipulator PD loops (Eq. 8), used as the inner loop beneath a DRL guidance policy.

Related Topics

• coordinated_base_manipulator_control — the coupled base+arm control this law realizes.
• generalized_inertia_matrix — the $M$ ($H$ in-source) inverted to cancel the dynamics.
• trajectory_tracking — the linearized error the PD loops drive to zero.
• ffsm_dynamics — the free-flying dynamics being feedback-linearized.

Open Questions

• dambrosio2024redundant reports nonzero PD steady-state error as the positioning bottleneck; does feedback linearization degrade near manipulator singularities where $M$ is ill-conditioned, and how does that interact with the redundant arm?