Foot-Ground Deviation (FGD)

Updated 5 July 2026

FGD is a family of metrics that quantifies the discrepancy between a foot’s intended support and its actual ground contact using signals like bump sensors, joint heights, and vGRFs.
In robotics, FGD reduction employs predictive control strategies that adjust ankle heights to minimize impact and ensure smooth swing-to-stance transitions.
In motion generation and cleanup, FGD serves as both a training reward and an evaluation metric to reduce issues like hovering, penetration, and foot slip.

Foot-Ground Deviation (FGD) denotes a measure of mismatch between a foot’s intended, predicted, or inferred relation to the ground and the relation actually realized or estimated at runtime. The term is not standardized across the literature. In online bipedal control, it can be expressed as a clearance error between an admittance-modified ankle height and a bump-sensor-based measurement of foot-ground proximity. In physics-aware dance generation, it is defined as a sequence-level deviation between the lowest body joint and a flat ground plane. In motion-contact estimation and cleanup, it appears naturally as a derived metric for hovering, penetration, and tangential slip during contact. In dense RGB-based foot-contact estimation, it is not named in the source paper, but the predicted foot contact probabilities, pixel height map, and ground normal make a paper-grounded geometric deviation measure directly computable (Abdolahnezhad et al., 2022, Jia et al., 14 Feb 2026, Mourot et al., 2022, Jung et al., 27 Nov 2025).

1. Terminological scope and family resemblance

FGD is best understood as a family of foot-ground consistency measures rather than a single canonical metric. The common structure is a discrepancy between a desired or expected support relation and a measured or inferred one. What changes across domains is the signal used to instantiate the discrepancy: foot-mounted proximity sensing in robotics, world-space joint height in generative motion, vGRF-conditioned contact geometry in animation cleanup, or image/mesh-ground geometry in dense contact estimation.

Work	Operational signal	FGD interpretation
(Abdolahnezhad et al., 2022)	Planned ankle height vs bump-sensor proximity	Online foot-ground clearance error
(Jia et al., 14 Feb 2026)	Lowest joint height vs flat ground	Sequence-level vertical deviation reward
(Mourot et al., 2022)	Contact labels, vGRFs, contact joints, ground plane	Derived hovering, penetration, and slip metric
(Jung et al., 27 Nov 2025)	Dense contact, pixel height map, ground normal	Grounded extension from contact to geometric deviation

This heterogeneity is methodologically important. In control-oriented robotics, FGD is a state error to be driven toward zero before touchdown. In diffusion-model fine-tuning, it is a reward shaping term that biases sampled motion toward physically plausible foot-ground interaction. In cleanup and estimation pipelines, it functions more naturally as an evaluation or post-processing criterion. A recurrent misconception is therefore to treat all reported “FGD” values as directly comparable; the underlying observables, temporal aggregation, and contact assumptions differ substantially across works.

2. Predictive clearance error in online bipedal locomotion

In “Online Bipedal Locomotion Adaptation for Stepping on Obstacles Using a Novel Foot Sensor” (Abdolahnezhad et al., 2022), the paper does not explicitly name FGD, but the sensing-and-control architecture makes a precise definition natural. Let $p_{z,mod}^{L,R}(t)$ be the planned ankle vertical position after admittance-force modification, and let $p_{z,m}^{L,R}(t)$ be the measured vertical foot-ground distance obtained from four spring-loaded bump sensors. Then

$FGD^{L,R}(t)=p_{z,mod}^{L,R}(t)-p_{z,m}^{L,R}(t),$

with $|FGD^{L,R}(t)|$ as the magnitude metric. An equivalent formulation is $FGD(t)=d_{des}(t)-d_{meas}(t)$ .

The sensing substrate is explicitly predictive. Four rotary contact “bump” sensors are mounted at the four corners of each foot. Each sensor is spring-loaded with a torsional spring, guided by fixed pins, protrudes below the sole, and compresses by up to $2$ cm when it encounters the ground or an obstacle before the main sole contacts it. The average proximity signal is

$d_{avg}^{L,R}(t)=\frac{d_A+d_B+d_C+d_D}{4},$

and the measured vertical foot-ground distance satisfies $p_{z,m}^{L,R}(t)\propto d_{avg}^{L,R}(t)$ . The bump-sensor foot-length controller is activated in a certain range of single support phase when the foot-ground distance is less than $2$ cm, written as $d_{avg}^{L,R}(t)\le d_{th}$ with $p_{z,m}^{L,R}(t)$ 0 m.

FGD reduction is embedded in a layered control stack. A first admittance layer balances vertical forces between legs using

$p_{z,m}^{L,R}(t)$ 1

followed by modified ankle heights

$p_{z,m}^{L,R}(t)$ 2

A second, predictive layer directly addresses near-ground FGD through

$p_{z,m}^{L,R}(t)$ 3

and

$p_{z,m}^{L,R}(t)$ 4

This drives $p_{z,m}^{L,R}(t)$ 5 toward $p_{z,m}^{L,R}(t)$ 6 before impact. In parallel, foot orientation adaptation uses the same four-sensor quartet to infer pitch and roll,

$p_{z,m}^{L,R}(t)$ 7

and reduces what the paper-faithful synthesis describes as angular FGD, namely the deviation between desired and actual foot-ground orientation. Desired angles are set to zero during straight walking so that the foot remains parallel to the ground.

The experiments situate FGD reduction in high-speed and obstacle-crossing regimes. Reported walking settings include speed $p_{z,m}^{L,R}(t)$ 8 km/h, step length $p_{z,m}^{L,R}(t)$ 9 cm, and step time $FGD^{L,R}(t)=p_{z,mod}^{L,R}(t)-p_{z,m}^{L,R}(t),$ 0 s. With the bump-sensor controller off, touchdown vertical forces are higher and the foot-ground distance profile closes more sharply; with the controller on, impact is “significantly reduced,” and the ankle tracks the modified trajectory well. On unseen inclined obstacles, the robot successfully steps over slope angles from $FGD^{L,R}(t)=p_{z,mod}^{L,R}(t)-p_{z,m}^{L,R}(t),$ 1 to $FGD^{L,R}(t)=p_{z,mod}^{L,R}(t)-p_{z,m}^{L,R}(t),$ 2 and obstacle heights up to $FGD^{L,R}(t)=p_{z,mod}^{L,R}(t)-p_{z,m}^{L,R}(t),$ 3 cm without reducing walking speed. The paper attributes hard impacts partly to foot position error caused by accumulative deflection in links and connections, and reports that the proposed framework drastically reduces these impacts. The practical significance is that FGD becomes a measurable online quantity whose reduction improves swing-to-stance smoothness without footstep replanning.

3. Sequence-level FGD reward in physically plausible dance generation

“Skeleton2Stage: Reward-Guided Fine-Tuning for Physically Plausible Dance Generation” gives the most explicit formulation of FGD among the cited works (Jia et al., 14 Feb 2026). Here FGD is not a local foot-sensor error but a sequence-level scalar derived from the lowest body joint’s height relative to a flat ground plane. For each frame $FGD^{L,R}(t)=p_{z,mod}^{L,R}(t)-p_{z,m}^{L,R}(t),$ 4, the method defines

$FGD^{L,R}(t)=p_{z,mod}^{L,R}(t)-p_{z,m}^{L,R}(t),$ 5

where $FGD^{L,R}(t)=p_{z,mod}^{L,R}(t)-p_{z,m}^{L,R}(t),$ 6 is the world-space vertical coordinate of joint $FGD^{L,R}(t)=p_{z,mod}^{L,R}(t)-p_{z,m}^{L,R}(t),$ 7. Over a sequence of $FGD^{L,R}(t)=p_{z,mod}^{L,R}(t)-p_{z,m}^{L,R}(t),$ 8 frames, the FGD reward is

$FGD^{L,R}(t)=p_{z,mod}^{L,R}(t)-p_{z,m}^{L,R}(t),$ 9

with constant ground height $|FGD^{L,R}(t)|$ 0. The reward decreases exponentially with the sequence-level $|FGD^{L,R}(t)|$ 1 deviation, so larger vertical mismatch yields smaller reward.

This design targets both penetration and floating. Because the lowest joint is used rather than a specific heel or toe marker, the reward is intentionally simple and global. During RL fine-tuning, the reward is normalized per music condition,

$|FGD^{L,R}(t)|$ 2

and enters the overall policy-gradient objective together with an imitation reward and an anti-freezing reward: $|FGD^{L,R}(t)|$ 3 The anti-freezing term is necessary because the physics-based rewards, including FGD, tend to push the model toward low-motion solutions with fewer anomalies.

FGD also appears at inference time as contact-gated guidance during diffusion sampling. The guidance energy is

$|FGD^{L,R}(t)|$ 4

and the predicted mean is updated by

$|FGD^{L,R}(t)|$ 5

where $|FGD^{L,R}(t)|$ 6 indicates contact according to the model’s predicted contact labels. Guidance is applied only during predicted contact frames, which preserves jumps and other non-contact phases. After sampling, a short post-processing step locks feet horizontally during predicted contact phases to eliminate foot-skating artifacts. The paper explicitly notes that horizontal skating is not part of the FGD reward itself.

The reported quantitative effects are substantial on AIST++ 20 s clips. The EDGE baseline yields $|FGD^{L,R}(t)|$ 7 and $|FGD^{L,R}(t)|$ 8, whereas Skeleton2Stage reports $|FGD^{L,R}(t)|$ 9 and $FGD(t)=d_{des}(t)-d_{meas}(t)$ 0. In the ablation focused on FGD, removing both FGD reward and guidance gives $FGD(t)=d_{des}(t)-d_{meas}(t)$ 1, removing only guidance gives $FGD(t)=d_{des}(t)-d_{meas}(t)$ 2, and the full method returns to $FGD(t)=d_{des}(t)-d_{meas}(t)$ 3. The same section reports that projection-based PhysDiff* variants perform worse in FGD and PFC and may fail through slipping or falling. The central significance of this formulation is that FGD becomes both a training reward and an inference-time energy, rather than merely a post hoc diagnostic.

4. Contact-conditioned FGD derived from vGRFs and IK cleanup

In “UnderPressure: Deep Learning for Foot Contact Detection, Ground Reaction Force Estimation and Footskate Cleanup,” the paper does not explicitly define FGD, but its methodology supports a rigorous derived formulation aligned with foot-ground consistency (Mourot et al., 2022). The core paper-defined object is the contact function $FGD(t)=d_{des}(t)-d_{meas}(t)$ 4, obtained from vertical ground reaction forces measured or estimated at the heel and toe. A location is in contact if its rescaled group vGRF is at least $FGD(t)=d_{des}(t)-d_{meas}(t)$ 5 of body weight, frames are discarded if total per-foot vGRF is below $FGD(t)=d_{des}(t)-d_{meas}(t)$ 6 of body weight, and contact phases shorter than $FGD(t)=d_{des}(t)-d_{meas}(t)$ 7 s are discarded. The network predicts per-cell vGRFs $FGD(t)=d_{des}(t)-d_{meas}(t)$ 8 from joint positions, after which $FGD(t)=d_{des}(t)-d_{meas}(t)$ 9 converts them to contact labels.

Given these ingredients, a paper-faithful FGD decomposition can be defined on the contact set $2$0. With ground plane $2$1, unit normal $2$2, ground point $2$3, and contact points $2$4, the unsigned vertical deviation is

$2$5

The same synthesis defines penetration-only and hover-only components by replacing the absolute value with $2$6 and $2$7, and defines a contact-phase horizontal slip term

$2$8

GRF-weighted variants are also natural because vGRFs are explicitly estimated and normalized.

The derived metric fits naturally with the paper’s cleanup pipeline. After estimating vGRFs and contacts, the method inserts “contact joints” below the foot joints at ground level and solves an optimization over joint rotations and root trajectory. The objective combines quaternion normalization, a foot-contact positional term that pins contact joints during contact phases, a trajectory-velocity preservation term, and a vGRF-invariance term implemented through the learned network. In the example settings reported by the paper, $2$9 optimization iterations are used with $d_{avg}^{L,R}(t)=\frac{d_A+d_B+d_C+d_D}{4},$ 0, $d_{avg}^{L,R}(t)=\frac{d_A+d_B+d_C+d_D}{4},$ 1, $d_{avg}^{L,R}(t)=\frac{d_A+d_B+d_C+d_D}{4},$ 2, and $d_{avg}^{L,R}(t)=\frac{d_A+d_B+d_C+d_D}{4},$ 3. Within this framework, reductions in hovering, penetration, and in-contact slip are precisely what an FGD-style metric would quantify before and after cleanup.

The broader empirical context is contact reliability. Overall F1 for contact detection is $d_{avg}^{L,R}(t)=\frac{d_A+d_B+d_C+d_D}{4},$ 4 for the main method, compared with $d_{avg}^{L,R}(t)=\frac{d_A+d_B+d_C+d_D}{4},$ 5 for the optimal threshold baseline; per-foot total vGRF RMSE is $d_{avg}^{L,R}(t)=\frac{d_A+d_B+d_C+d_D}{4},$ 6 of body weight overall; and on blended motions the mean velocity of the feet during contact phases is approximately halved after cleanup. These results do not report FGD explicitly, but they indicate that the paper’s learned vGRF estimation and IK constraints provide the signals and operators needed to instantiate FGD as a physically grounded consistency measure.

5. Dense foot-ground geometry from a single RGB image

“Shoe Style-Invariant and Ground-Aware Learning for Dense Foot Contact Estimation” does not explicitly define or use the term FGD (Jung et al., 27 Nov 2025). It focuses on dense foot contact estimation from a single RGB image. Nevertheless, the framework supplies a direct geometric basis for an FGD measure because it predicts dense foot contact probabilities over a foot mesh, a foot segmentation mask, a pixel height map, and a global ground normal in camera coordinates.

The FECO representation is unusually rich for this purpose. The dense contact output is defined on an SMPL-X foot subset with $d_{avg}^{L,R}(t)=\frac{d_A+d_B+d_C+d_D}{4},$ 7 vertices. The ground-aware branch predicts a per-pixel height-above-ground map in pixel units, scaled by $d_{avg}^{L,R}(t)=\frac{d_A+d_B+d_C+d_D}{4},$ 8, and a unit ground normal. A principled 3D FGD, when camera geometry and 3D foot vertices are available, is the probability-weighted plane distance

$d_{avg}^{L,R}(t)=\frac{d_A+d_B+d_C+d_D}{4},$ 9

where $p_{z,m}^{L,R}(t)\propto d_{avg}^{L,R}(t)$ 0 are the per-vertex contact probabilities. Region-wise heel, midfoot, and toe variants follow directly by restricting the index set. Without calibration, an image-space analogue is

$p_{z,m}^{L,R}(t)\propto d_{avg}^{L,R}(t)$ 1

or a contact-probability-weighted version if a contact map or region weights are used. In this setting, FGD is a clearance proxy rather than a directly metric world-space distance.

The method’s architectural choices are designed to stabilize precisely the signals that make such a definition meaningful. Shoe style adversarial training promotes style-invariant contact features, while ground-aware learning injects ground information through the pixel height map, ground normal, and spatial attention fusion. This suggests that FECO is not merely estimating whether contact exists, but learning a representation from which foot-ground deviation can be quantified densely over the support surface.

The paper reports state-of-the-art dense contact accuracy on MMVP, with Precision $p_{z,m}^{L,R}(t)\propto d_{avg}^{L,R}(t)$ 2, Recall $p_{z,m}^{L,R}(t)\propto d_{avg}^{L,R}(t)$ 3, and F1 $p_{z,m}^{L,R}(t)\propto d_{avg}^{L,R}(t)$ 4, compared with $p_{z,m}^{L,R}(t)\propto d_{avg}^{L,R}(t)$ 5 for POSA, $p_{z,m}^{L,R}(t)\propto d_{avg}^{L,R}(t)$ 6 for BSTRO, and $p_{z,m}^{L,R}(t)\propto d_{avg}^{L,R}(t)$ 7 for DECO. Ground-aware learning raises F1 from $p_{z,m}^{L,R}(t)\propto d_{avg}^{L,R}(t)$ 8 to $p_{z,m}^{L,R}(t)\propto d_{avg}^{L,R}(t)$ 9, and the supplementary results include F1 $2$0 on BEHAVE and $2$1 on Hi4D. These are contact metrics rather than FGD measurements, but a plausible implication is that improved dense contact accuracy reduces foot-ground mismatch and strengthens any FGD computed from the same outputs.

6. Comparative interpretation, assumptions, and recurrent misconceptions

Across these works, FGD is best treated as a domain-specific observable tied to the sensing modality and task objective, not as a universal benchmark. In the bipedal robot, FGD is local, online, and predictive: it is minimized in the last $2$2 cm before contact and augmented by an orientation controller and a ZMP-CoM admittance layer. In Skeleton2Stage, FGD is global over time, defined on the lowest joint rather than explicit foot markers, and used both as an RL reward and as contact-gated test-time guidance. In UnderPressure, FGD is not reported by the paper but emerges naturally from vGRF-derived contact labels, a ground-plane model, and contact-joint kinematics. In FECO, FGD is likewise absent as a named quantity, but the combination of dense contact and ground-aware geometry makes it directly definable (Abdolahnezhad et al., 2022, Jia et al., 14 Feb 2026, Mourot et al., 2022, Jung et al., 27 Nov 2025).

Several misconceptions follow from ignoring these distinctions. First, FGD is not synonymous with footskate. Skeleton2Stage explicitly separates horizontal skating from FGD and suppresses it via post-processing during predicted contact. UnderPressure, by contrast, motivates an FGD decomposition in which tangential slip is a first-class component. Second, FGD is not always a contact-only quantity. In the robot controller, the critical regime is the pre-touchdown interval, where predictive sensing reduces impact before the sole lands. Third, FGD is not always tied to explicit foot landmarks. Skeleton2Stage uses the lowest body joint per frame, which sacrifices anatomical specificity for simplicity and differentiability.

The main assumptions and limitations are correspondingly diverse. The robot controller’s predictive window is limited to the final $2$3 cm before contact, and the authors note coverage failures when obstacles miss the corner bump sensors. Skeleton2Stage assumes a flat ground plane and does not disclose $2$4 or the guidance schedule $2$5. UnderPressure requires ground-plane estimation or assumption, and a single global plane is invalid on stairs or obstacles unless local phase-wise heights are used. FECO does not provide camera calibration, so image-space FGD remains in pixel units unless external geometry is available. These limitations do not undermine the concept; rather, they show that FGD is inseparable from the measurement model used to instantiate the foot-ground relation.

In the broader technical sense, FGD formalizes a core problem shared by legged robotics, physically plausible motion generation, animation cleanup, and contact-aware perception: the foot must neither arrive too early nor too late, neither float nor penetrate, and neither twist nor slide incompatibly with support. The literature surveyed here shows that once the relevant support signal is available—bump compression, joint height, vGRF-derived contact, or dense ground-aware geometry—FGD becomes a compact way to encode foot-ground consistency and to drive control, learning, or post-processing toward smoother and more physically credible contact.