Center-of-Mass-Aware Control

• Center-of-Mass-Aware Control is a class of methods that explicitly models and regulates the centroidal state (e.g., position, momentum, wrench) to improve system stability and performance.
• It integrates estimation, feedback, and optimization techniques, employing methods like gradient descent and online learning to reduce errors in CoM tracking.
• Applications span humanoid locomotion, multi-contact manipulation, and reconfigurable aerial and buoyant platforms, demonstrating quantifiable gains in stability and control.

Center-of-mass-aware control denotes a class of control methods that explicitly model, estimate, regulate, or optimize the center of mass (CoM), centroidal momentum, CoM-dependent wrench, or CoM-feasibility region of a physical system. In the cited literature, this includes asymptotic stabilization of centroidal momentum for an underactuated flying humanoid (Pucci et al., 2017), online CoM learning for a wheeled inverted pendulum humanoid (Zafar et al., 2018), direct centroidal locomotion using a five-mass model (Ficht et al., 2022), wrench-aware admittance control for unknown-payload manipulation (Gholampour et al., 21 Apr 2026), whole-body control with an online geometric CoM balance region in multiple unilateral contacts (Roux et al., 2021), and platforms whose internal mechanisms reconfigure the CoM to enlarge the feasible wrench set or to improve task-dependent tracking (Hui et al., 2024, Wang et al., 2 May 2026, Liu et al., 27 May 2025).

1. Core quantities and problem formulations

A recurring formulation is to treat the CoM and centroidal dynamics as the minimal physically meaningful state on which control is designed. For a free-floating multibody system, the robot CoM position is $p_c$, its velocity is $v_c = \dot{p}_c$, and the centroidal momentum is

$$h=\begin{bmatrix} h_\ell \ h_\omega \end{bmatrix}, \qquad h_\ell = m v_c,$$

with a centroidal momentum matrix $A(q)$ such that $h=A(q)\nu$. In the flying humanoid setting, the centroidal momentum dynamics split into

$$\dot{h}_\ell = \sum_{k=1}^4 f_k + m g, \qquad \dot{h}_\omega = \sum_{k=1}^4 (r_k-p_c)\times f_k,$$

so the sum of external forces drives CoM linear momentum and the moment arms of those forces drive angular momentum (Pucci et al., 2017). In the wheeled inverted pendulum humanoid setting, the central balancing condition is expressed as

$x_{\text{com}}(q)=0,$

and the CoM itself is parameterized linearly as

$x_{\text{com}}(q)=\phi(q)^\top \beta,$

which condenses masses and mass-times-CoM coordinates into a single parameter vector $\beta$ (Zafar et al., 2018).

In multi-contact humanoid control, CoM feasibility is formulated geometrically. If $\mathcal{X}$ denotes the set of contact forces and CoM positions satisfying Newton–Euler equilibrium together with unilateral and friction constraints, then the balance region is the projection

$v_c = \dot{p}_c$0

and is used online as a polyhedral inclusion constraint $v_c = \dot{p}_c$1 inside a whole-body QP (Roux et al., 2021). For biped balance with CoM height variations, the inverted pendulum model

$v_c = \dot{p}_c$2

introduces a time-varying stiffness $v_c = \dot{p}_c$3, and the associated boundedness condition quantifies the capturability of 3D CoM trajectories (Caron et al., 2017).

This suggests that CoM-aware control is not limited to direct CoM position tracking. Depending on the system, the regulated variable can be linear momentum, angular momentum, CoM inclusion in a feasible region, a CoM-dependent restoring term, or a CoM-dependent contact wrench.

2. Estimation and identification

CoM-aware control depends on estimating the centroidal state with sufficient fidelity for feedback and planning. In human motion analysis, three estimation methods were compared: "Pelvis Markerset", "Whole-Body Markerset", and "Whole-Body Markerset & GRFs". Using the RMS of the external force residual as a performance metric, the "Pelvis Markerset" method showed 96% to 104% higher RMS external force residual values during dynamic activities compared to the two whole-body methods, while "Whole-Body Markerset & GRFs" was similar to "Whole-Body Markerset" (Peng et al., 2024). The corresponding dynamic consistency test was

$v_c = \dot{p}_c$4

which directly measures whether the estimated CoM acceleration is consistent with measured external forces (Peng et al., 2024).

In online balancing for a wheeled inverted pendulum humanoid, the CoM is estimated by learning the parameter vector $v_c = \dot{p}_c$5 in the linear model $v_c = \dot{p}_c$6. The cost function

$v_c = \dot{p}_c$7

is minimized by gradient descent,

$v_c = \dot{p}_c$8

while Active Disturbance Rejection Control keeps the robot balanced despite current mass-model errors (Zafar et al., 2018). In hardware, the mean CoM error over 46 test poses decreased from 2.5 cm to 0.4 cm, and the max error decreased from 6 cm to 1.2 cm after 190 gradient steps (Zafar et al., 2018).

Unknown-payload manipulation introduces a different estimation problem: the payload CoM offset relative to the tool center point generates an offset wrench at the wrist. Under a pure-translation assumption,

$v_c = \dot{p}_c$9

which yields a two-stage identification procedure. Mass is estimated by

$$h=\begin{bmatrix} h_\ell \ h_\omega \end{bmatrix}, \qquad h_\ell = m v_c,$$0

and the payload CoM offset is identified from

$$h=\begin{bmatrix} h_\ell \ h_\omega \end{bmatrix}, \qquad h_\ell = m v_c,$$1

In a representative trial, the X-offset estimate achieved 3.5 mm RMSE and the TCP x-position achieved 1.2 mm RMSE during online estimation (Gholampour et al., 21 Apr 2026).

For hardware-constrained humanoids, a five-mass estimator combines IMU data with approximate dynamics of each mass to obtain an accurate assessment of the centroidal state and Center of Pressure even when direct forms of force or contact sensing are unavailable (Ficht et al., 2023). The improved estimator explicitly corrects the difference between IMU acceleration and torso-CoM acceleration and then incorporates limb accelerations into the whole-body CoM acceleration estimate (Ficht et al., 2023).

3. Feedback and optimization in locomotion and balancing

A canonical CoM-aware control law appears in flying humanoids, where the control objective is defined as the asymptotic stabilization of the robot centroidal momentum. With momentum error $$h=\begin{bmatrix} h_\ell \ h_\omega \end{bmatrix}, \qquad h_\ell = m v_c,$$2, the desired momentum-rate command is

$$h=\begin{bmatrix} h_\ell \ h_\omega \end{bmatrix}, \qquad h_\ell = m v_c,$$3

and the thrust forces are computed from

$$h=\begin{bmatrix} h_\ell \ h_\omega \end{bmatrix}, \qquad h_\ell = m v_c,$$4

Under the feasibility and full-state assumptions stated in the paper, Lyapunov analysis yields asymptotic convergence of $$h=\begin{bmatrix} h_\ell \ h_\omega \end{bmatrix}, \qquad h_\ell = m v_c,$$5 to $$h=\begin{bmatrix} h_\ell \ h_\omega \end{bmatrix}, \qquad h_\ell = m v_c,$$6 (Pucci et al., 2017). Because $$h=\begin{bmatrix} h_\ell \ h_\omega \end{bmatrix}, \qquad h_\ell = m v_c,$$7, regulating linear momentum is directly equivalent to regulating CoM velocity (Pucci et al., 2017).

In humanoid locomotion, "Direct Centroidal Control for Balanced Humanoid Locomotion" uses a five-mass description of a humanoid and generates whole-body motions from desired foot trajectories and centroidal parameters of the robot (Ficht et al., 2022). The controller regulates both CoM motion and the orientation of the principal axes of inertia, uses a set of simplified models to formulate general and intuitive control laws, and requires only a 6-axis IMU and joint encoders for implementation (Ficht et al., 2022). The locomotion controller combines LIPM-based CoM feedback, end-of-step prediction, and an augmented CoM formulation that couples CoM motion with inertia orientation (Ficht et al., 2022).

A complementary formulation is the convex boundedness approach for 3D CoM control with height variations. The key change of variable is

$$h=\begin{bmatrix} h_\ell \ h_\omega \end{bmatrix}, \qquad h_\ell = m v_c,$$8

which turns infinite-horizon boundedness conditions into finite-interval constraints on $$h=\begin{bmatrix} h_\ell \ h_\omega \end{bmatrix}, \qquad h_\ell = m v_c,$$9 and thereby on $A(q)$0. The vertical boundedness condition becomes

$A(q)$1

and a capture-point-like CoP law emerges as

$A(q)$2

The resulting optimization is low-dimensional and solvable fast enough for real-time control; the reported computation times are approximately $A(q)$3 ms in 2D and $A(q)$4 ms in 3D (Caron et al., 2017).

For hardware-constrained humanoids, centroidal estimation is paired with feedforward and feedback control that compensate for insufficient joint tracking capabilities and lack in Degrees of Freedom (Ficht et al., 2023). The feedforward layer adjusts CoM-to-foot relationships, swing-foot timing, and inertia orientation, while the feedback layer combines CoM/CMP regulation, tilt-compensating step feedback, and End Of Step re-planning (Ficht et al., 2023). The whole approach allows for reactive stepping to maintain balance despite these limitations, and simulation results show higher disturbance rejection than the Capture Steps baseline across a range of push magnitudes (Ficht et al., 2023).

Taken together, these methods show a common structure: CoM-aware control is usually split into a centroidal layer that reasons in low-dimensional physical variables and a whole-body layer that realizes the resulting motion under kinematic, dynamic, or hardware constraints.

4. Contact-rich manipulation and multi-contact whole-body control

In manipulation, CoM awareness often enters through the distinction between environmental wrenches and payload-induced wrenches. "Wrench-Aware Admittance Control for Unknown-Payload Manipulation" models the wrist wrench as

$A(q)$5

where $A(q)$6 is induced by the unknown payload mass, CoM offset, and inertia (Gholampour et al., 21 Apr 2026). The translational admittance law is

$A(q)$7

and the method sets

$A(q)$8

so that payload-induced forces are not misinterpreted as environment contact (Gholampour et al., 21 Apr 2026). After estimating the CoM offset $A(q)$9, the placement command is corrected at the object-CoM level: $h=A(q)\nu$0 For a representative trial, the correction-command error was 2.73 mm, the actual release error versus the ideal was 3.38 mm, and the execution error versus command was 1.03 mm (Gholampour et al., 21 Apr 2026). The same principle extends to stacking by adding the vertical layer offset $h=A(q)\nu$1 (Gholampour et al., 21 Apr 2026).

In multi-contact humanoid control, the CoM itself becomes a decision variable constrained by an online geometric balance region. The paper on multiple fixed and moving unilateral contacts improves the computational performance of the geometric center-of-mass inclusion-based balance method and integrates such a balance region with relevant contact force distribution without pre-computing a target center-of-mass (Roux et al., 2021). The balance region is computed from Newton–Euler equilibrium, unilateral contact, and Coulomb friction, then inserted directly into the whole-body control framework as a polyhedral inclusion $h=A(q)\nu$2 (Roux et al., 2021). A CoM admittance law

$h=A(q)\nu$3

biases the CoM velocity so that whole-body motion supports force regulation while the CoM remains in the admissible region (Roux et al., 2021).

These two lines of work emphasize that contact-rich CoM-aware control is not only about keeping the CoM in a safe zone. It also uses CoM motion to disambiguate contact versus payload effects, to improve placement and stacking, and to expand the feasible set of contact-force distributions under unilateral and frictional constraints.

5. Reconfigurable CoM in aerial, buoyant, and transformable platforms

Several recent systems turn the CoM itself into an actuated resource. "AEROBULL: A Center-of-Mass Displacing Aerial Vehicle Enabling Efficient High-Force Interaction" introduces a 3.12 kg aerial platform with tiltable rotors with 5-DoF actuation, a shifting-mass mechanism that dynamically adjusts the system’s CoM during contact-based task execution, and a compliant end-effector (Hui et al., 2024). Physical experiments show that, with a total mass of 3.12 kg, the UAV exerted a maximum pushing force of above 28 N being almost equal to its gravity force, and that displaced CoM outperformed a fixed CoM configuration in high-force interaction (Hui et al., 2024). A closely related platform design study reports that the proposed system, weighing 3.12 kg, was able to stably exert over 28 N of force on a work surface, nearly equivalent to its gravitational force, achieved solely through the tilting of its back rotors, and introduces the normalized force factor

$h=A(q)\nu$4

for comparing aerial force-generation capability (Hui et al., 2024).

Underactuated buoyant systems use the same idea at a different time scale. In "Bi-Level Reinforcement Learning Control for an Underactuated Blimp via Center-of-Mass Reconfiguration", a movable internal slider reconfigures the CoM relative to the center of buoyancy, which changes the inertia matrix, Coriolis terms, gravity–buoyancy restoring term, and control allocation matrix (Wang et al., 2 May 2026). The slider moves within $h=A(q)\nu$5 cm and is selected once per episode by an outer policy, while an inner Soft Actor-Critic policy generates thrust commands (Wang et al., 2 May 2026). Across a 27-goal evaluation set, the proposed method achieved an overall cross-track RMSE of $h=A(q)\nu$6 in units of $h=A(q)\nu$7 m, compared with $h=A(q)\nu$8 for the best fixed-CoM SAC baseline and $h=A(q)\nu$9 for PID-SPG (Wang et al., 2 May 2026). The learned mapping depends primarily on target height: higher targets lead to backward slider positions and lower targets lead to forward slider positions (Wang et al., 2 May 2026).

A terrestrial analogue appears in the unmanned deformable vehicle, a wheel-legged robot transforming between vehicular and humanoid states. The platform adds a two-degree-of-freedom center-of-mass adjustment mechanism and a motion stability hierarchical control algorithm (Liu et al., 27 May 2025). In vehicular state, a Fuzzy-PID controller on the X slider changes the stability factor from 0.00097 to 0.0024 by moving the slider by $$\dot{h}_\ell = \sum_{k=1}^4 f_k + m g, \qquad \dot{h}_\omega = \sum_{k=1}^4 (r_k-p_c)\times f_k,$$0 m; in humanoid state, walking stability is improved by controlling the slider motion through a variable-universe fuzzy controller combined with ADRC (Liu et al., 27 May 2025).

These platforms treat CoM not merely as a state to be estimated or regulated, but as a structural actuator or morphology variable. This suggests a broader design pattern in which internal reconfiguration modifies the closed-loop physics before fast control is applied.

6. Limitations, misconceptions, and broader interpretations

The literature also delineates the boundaries of CoM-aware control. In unknown-payload manipulation, the estimation model assumes a rigid grasp, pure translation during estimation, negligible angular velocity and acceleration, sufficient excitation for rank-3 identification, and accurate force-torque and acceleration sensing; CoM estimation is restricted to translational segments and does not explicitly model $$\dot{h}_\ell = \sum_{k=1}^4 f_k + m g, \qquad \dot{h}_\omega = \sum_{k=1}^4 (r_k-p_c)\times f_k,$$1 (Gholampour et al., 21 Apr 2026). In online CoM learning for the wheeled inverted pendulum humanoid, the hardware experiments use manual pose execution and offline gradient descent, and the method assumes known kinematics while adapting only link masses and CoM locations (Zafar et al., 2018). In multi-contact balance-region control, linearized friction cones make the feasible region conservative even though the computational gain is substantial (Roux et al., 2021).

A persistent misconception is that adding more sensing channels necessarily improves CoM estimation. The comparison of "Pelvis Markerset", "Whole-Body Markerset", and "Whole-Body Markerset & GRFs" shows the opposite in one important regime: when high-quality whole-body kinematics are already available, incorporating GRFs through the presented Kalman filter does not improve the estimates from whole-body kinematics (Peng et al., 2024). Another misconception is that CoM-aware control is equivalent to choosing a single “best” CoM target. The multi-contact whole-body formulation explicitly avoids pre-computing a target center-of-mass, and the blimp results show that no single fixed CoM works best for all goal heights (Roux et al., 2021, Wang et al., 2 May 2026).

The concept also extends beyond robot actuation. In human walking, the phase shift between left and right foot contacts acts as an implicit CoM regulation variable: when the time of one foot's initial contact falls right in the middle of the other foot's stride cycle, the dispersion of ground reaction force, CoM acceleration, velocity, displacement, and average kinetic energy reaches extrema, and the total average CoM kinetic energy is minimized at $$\dot{h}_\ell = \sum_{k=1}^4 f_k + m g, \qquad \dot{h}_\omega = \sum_{k=1}^4 (r_k-p_c)\times f_k,$$2 (Fan et al., 2010). In internal density functional theory for self-bound quantum systems, CoM correlations are encoded by a dedicated local CoM-correlation functional and corresponding local potential, so that CoM separation is enforced in an internal coordinate description rather than corrected afterward (Messud, 2012).

Across these domains, center-of-mass-aware control is best understood as a family of methods that elevate centroidal quantities from by-products of motion to primary variables of estimation, optimization, and feedback. The common thread is physical structure: CoM-aware controllers exploit the fact that translation, rotation, contact wrench, and stability are coupled through the centroidal state, and they use that coupling directly rather than treating it as a disturbance.