MorFiC: Fixing Value Miscalibration for Zero-Shot Quadruped Transfer

Prakhar Mishra; Amir Hossain Raj; Xuesu Xiao; Dinesh Manocha

cs.ROMar 15, 2026

MorFiC: Fixing Value Miscalibration for Zero-Shot Quadruped Transfer

Authors: Prakhar Mishra, Amir Hossain Raj, Xuesu Xiao, Dinesh Manocha

Organizations: University of Maryland, College Park, MD, USA · George Mason University, Fairfax, VA, USA

Abstract

Generalizing learned locomotion policies across quadrupedal robots with different morphologies remains a challenge. Policies trained on a single robot often fail when deployed on embodiments with different mass distributions, kinematics, joint limits, or actuation constraints, forcing per-robot retraining. Prior works have approached this primarily either by scaling via training across real or generated embodiments or using large architectures producing transferable policies which are both storage and compute heavy. We argue that both of these approaches circumvent a key failure mode in actor-critic learning: a shared value function tends to average incompatible value targets across embodiments, yielding miscalibrated advantages and fixing that helps transfer and reduce the compute cost. We present MorFiC, a reinforcement learning approach for zero-shot cross-morphology locomotion which fixes this issue using multiplicative critic conditioning on a morphology latent. Trained with a single source robot with morphology randomization in simulation, MorFiC achieves zero-shot transfer to total seven robots and reaching forward velocity competitive or surpassing scaling-based and morphology-conditioned PPO baselines for examples 1.98 m/s on AlienGo, where as additive PPO baselines remain below 0.65 m/s. MorFiC achieves this using single training robot within 2 hours of training time compared to tens or hundreds of hours required for scaling baselines training on multiple embodiments. We diagnose critic calibration via three metric: Explained variance, advantage sign-flip rate and policy gradient cosine, confirming our critic conditioning as determinant for policy update direction. Finally, we demonstrate zero-shot deployment on Unitree Go1 and Go2 robots without fine-tuning.

Figures & tables

Figure 2: MorFiC Architecture. A morphology descriptor $m\sim p(m)$ is sampled, encoded via a morphology latent $z=f(m)$ ; and used to modulate the crtic via multiplicative conditioning; actor is also conditioned via same $z$ .

Panel of Figure 3 — Figure 3: Critic calibration under morphology shift. Left: EV for internal PPO variants. Right: external baselines. Higher EV or closer to 1 is better.

Panel of Figure 4 — Figure 4: Left: Compute cost (in hours) and total training timesteps used. Right: Performance w.r.t. normalized morphology distance. MorFiC performs better than both external and PPO baselines.

Target	PPO $\bar{v}_{x}\pm\sigma/S$	Actor-only $\bar{v}_{x}\pm\sigma/S$	Actor+Critic $\bar{v}_{x}\pm\sigma/S$	MorFiC-F $\bar{v}_{x}\pm\sigma/S$
Go2	$1.79{\pm}0.31/0.984$	$0.88{\pm}0.23/0.265$	$1.70{\pm}0.30/0.891$	$\mathbf{2.04{\pm}0.37}/\mathbf{0.984}$
Go1	$1.93{\pm}0.27/\mathbf{0.906}$	$1.49{\pm}0.36/0.594$	$1.82{\pm}0.32/0.859$	$\mathbf{2.06{\pm}0.46}/0.547$
A1	$1.41{\pm}0.42/0.406$	$0.01{\pm}0.06/0.000$	$1.52{\pm}0.27/0.422$	$\mathbf{2.14{\pm}0.36}/\mathbf{0.516}$
AlienGo	$0.27{\pm}0.07/0.000$	$0.64{\pm}0.26/\mathbf{1.000}$	$0.40{\pm}0.18/0.156$	$\mathbf{1.98{\pm}0.51}/\mathbf{1.000}$
B1	$0.21{\pm}0.06/\mathbf{1.000}$	$0.04{\pm}0.07/\mathbf{1.000}$	$0.12{\pm}0.07/\mathbf{1.000}$	$\mathbf{0.22{\pm}0.08}/\mathbf{1.000}$
Cheetah	$0.68{\pm}0.51/0.282$	$0.32{\pm}0.49/\mathbf{1.000}$	$1.28{\pm}0.58/0.382$	$\mathbf{1.39{\pm}0.69}/0.422$

Table 2: Zero-shot cross-morphology transfer. Training is on Go2. Each cell reports

\bar{v}_{x}\pm\sigma/S

, where

\bar{v}_{x}

is forward speed in m/s and

S

is survival rate. Bold denotes the best speed and survival rate. We run all the PPO variants with

{v}^{cmd}_{x}=2.0

m/s for all 7 robots. All the experiments run for

500

time-steps on total 64 environments.

Target	URMA $\bar{v}_{x}{\pm}\sigma/S$	BodyTrans. $\bar{v}_{x}{\pm}\sigma/S$	GenLoco $\bar{v}_{x}{\pm}\sigma/S$	Embod. $\bar{v}_{x}{\pm}\sigma/S$	MorFiC-F $\bar{v}_{x}{\pm}\sigma/S$
Go2	$1.84{\pm}0.26/\mathbf{1.000}$	$0.30{\pm}0.21/0.656$	$0.59{\pm}0.05/0.922$	$1.23{\pm}0.06/0.906$	$\mathbf{2.04{\pm}0.37}/0.984$
Go1	$1.93{\pm}0.28/\mathbf{1.000}$	$0.21{\pm}0.13/\mathbf{1.000}$	$0.98{\pm}0.01/\mathbf{1.000}$	$1.94{\pm}0.09/0.953$	$\mathbf{2.06{\pm}0.46}/0.547$
A1	$1.79{\pm}0.25/\mathbf{1.000}$	$0.39{\pm}0.15/0.421$	$0.92{\pm}0.01/\mathbf{1.000}$	$1.86{\pm}0.08/0.906$	$\mathbf{2.14{\pm}0.36}/0.516$
AlienGo	$-/-$	$0.30{\pm}0.28/0.234$	$0.96{\pm}0.03/\mathbf{1.000}$	$0.41{\pm}0.08/0.000$	$\mathbf{1.98{\pm}0.51}/\mathbf{1.000}$
B1	$-/-$	$0.04{\pm}0.11/0.796$	$0.00/0.000$	$\mathbf{2.86{\pm}0.11}/0.969$	$0.21{\pm}0.08/\mathbf{1.000}$
Cheetah	$-/-$	$-/\mathbf{1.000}$	$0.73{\pm}0.06/0.969$	$0.06{\pm}0.09/0.000$	$\mathbf{1.39{\pm}0.69}/0.422$

Table 3: External baselines vs. MorFiC.

\bar{v}_{x}\pm\sigma/S

(m/s; survival). – = no forward motion.

v_{x}^{\mathrm{cmd}}=2.0

m/s (GenLoco: no

v_{x}^{\mathrm{cmd}}

input). Bold = best.

Target	MorFiC-F $\bar{v}_{x}{\pm}\sigma/S$	MorFiC-F(Scaled) $\bar{v}_{x}{\pm}\sigma/S$	MorFiC-H $\bar{v}_{x}{\pm}\sigma/S$	MorFiC-A $\bar{v}_{x}{\pm}\sigma/S$
Go2	$2.04{\pm}0.37/0.984$	$2.03{\pm}0.26/0.875$	$\mathbf{2.10{\pm}0.28}/0.953$	$2.03{\pm}0.19/\mathbf{1.000}$
Go1	$\mathbf{2.06{\pm}0.46}/0.647$	$1.98{\pm}0.34/0.823$	$1.99{\pm}0.31/0.766$	$1.99{\pm}0.35/\mathbf{0.853}$
A1	$\mathbf{2.14{\pm}0.36}/0.516$	$2.04{\pm}0.24/0.531$	$2.02{\pm}0.26/\mathbf{0.766}$	$1.76{\pm}0.26/0.609$
AlienGo	$\mathbf{1.98{\pm}0.51}/\mathbf{1.000}$	$1.78{\pm}0.45/\mathbf{1.000}$	$1.75{\pm}0.46/\mathbf{1.000}$	$1.79{\pm}0.52/\mathbf{1.000}$
B1	$\mathbf{0.21{\pm}0.08}/\mathbf{1.000}$	$0.18{\pm}0.08/\mathbf{1.000}$	$0.20{\pm}0.03/\mathbf{1.000}$	$0.18{\pm}0.06/\mathbf{1.000}$
Cheetah	$1.39{\pm}0.69/0.422$	$\mathbf{1.97{\pm}0.62}/0.359$	$1.61{\pm}0.45/0.344$	$1.57{\pm}0.56/\mathbf{0.703}$

Table 4: Ablation Table. Each cell reports

\bar{v}_{x}\pm\sigma/S

, where

\bar{v}_{x}

is forward speed in m/s and

S

is survival rate. Alive time is omitted. Bold denotes the best speed per target robot.

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Target	Expanded range $v_{x}^{\max}{\pm}\sigma/S$	FiLM $v_{x}^{\max}{\pm}\sigma/S$
Go2	$1.9013{\pm}0.3510/0.8531$	$\mathbf{2.0415{\pm}0.3670}/\mathbf{0.9844}$
Go1	$1.9208{\pm}0.3087/\mathbf{0.7656}$	$\mathbf{2.0649{\pm}0.4552}/0.5469$
A1	$1.8241{\pm}0.2322/\mathbf{0.7596}$	$\mathbf{2.1404{\pm}0.3608}/0.5156$
AlienGo	$1.5499{\pm}0.5078/\mathbf{1.0000}$	$\mathbf{1.9812{\pm}0.5146}/\mathbf{1.0000}$
B1	$0.2001{\pm}0.0215/\mathbf{1.0000}$	$\mathbf{0.2109{\pm}0.0768}/\mathbf{1.0000}$
Cheetah	$1.2362{\pm}0.4805/0.3348$	$\mathbf{1.3922{\pm}0.6902}/\mathbf{0.4219}$

Appendix

Table 6: Effect of expanded morphology ranges and FiLM conditioning. Each entry reports

v_{x}^{\max}\pm\sigma/S

, where

S

denotes survival rate. Bold indicates the higher value for each metric independently; ties are bolded for both methods.

Stream	Signals	Dim
$o_{t}$	$[\,v,\ \omega,\ g_{\text{proj}},\ c,\ q-q_{0},\ \dot{q},\ a_{t-1}\,]$	48
$h_{t}$	$\{o_{t-k}\}_{k=1}^{15}$	$15\times 48$
$p_{t}$	$[\mu_{\text{fric}},\ e,\ m_{\text{base}},\ \Delta c,\ \mu_{\text{joint}}]$	18
$z_{m}$	morphology encoder output	$d=11$

Appendix

Table 7: Observation streams used for policy and value learning.

Module	Specification
Actor MLP	$[\text{obs history},\hat{z}_{\mathrm{priv}},z_{m}]\rightarrow[512,256,128]\rightarrow a$ , ELU
Critic trunk	$[\text{obs history},z_{\mathrm{priv}}]\rightarrow[512,256,128]\rightarrow V$ , ELU
Critic trunk (FiLM scaled)	$[\text{obs history},z_{\mathrm{priv}}]\rightarrow[1024,512,256]\rightarrow V$ , ELU
Initial action std.	$\sigma_{0}=1.0$
Adaptation module	$\text{obs history}\rightarrow[256,128]\rightarrow\hat{z}_{\mathrm{priv}}$ , ELU
Student latent dropout	$p=0.2$ during training

Appendix

Table 8: Policy, critic, and morphology-conditioning architecture used in MorFiC. The PPO optimizer and rollout hyperparameters are shared across all methods and reported separately in Table 10 .

Variant	Critic conditioning	Key detail
Vanilla PPO	None	Critic does not receive morphology information
Concat- $z$	Direct concatenation	$z_{m}$ is appended to the critic input
FiLM	Feature-wise modulation	$h\leftarrow h(1+\gamma)+\beta$
Scaled FiLM	Residual FiLM with scale	FiLM outputs multiplied by $0.1$
AdaLN	LayerNorm + FiLM	$h\leftarrow\mathrm{LN}(h)$ before FiLM modulation
HyperNet	Low-rank residual adapter	$h\leftarrow Wh+B_{z}A_{z}h$ , rank $16$ , scale $0.1$

Appendix

Table 9: Morphology-conditioning variants evaluated in the ablation study. All variants use the same PPO settings and base actor–critic widths as Table 8 .

PPO setting	Value
Discount $\gamma$	0.99
GAE $\lambda$	0.95
Clip $\epsilon$	0.2
Entropy coeff.	0.01
Value loss coeff.	1.0
Clipped value loss	True

Appendix

Table 10: PPO hyperparameters used in all baseline and MorFiC experiments.

Term	Definition	Weight
$r_{\text{lin}}$	$4\exp\!\left(-\frac{\\|\mathbf{v}^{cmd}_{xy}-\mathbf{v}_{xy}\\|^{2}}{\sigma_{\text{lin}}}\right)$	$w_{\text{lin}}$
$r_{\text{yaw}}$	$\exp\!\left(-\frac{(\omega^{cmd}_{z}-\omega_{z})^{2}}{\sigma_{\text{yaw}}}\right)$	$w_{\text{yaw}}$
$p_{v_{z}}$	$(v_{z})^{2}$	$w_{v_{z}}$
$p_{\omega_{xy}}$	$\\|\boldsymbol{\omega}_{xy}\\|^{2}$	$w_{\omega}$
$p_{\text{ori}}$	$\\|\hat{\mathbf{g}}_{xy}\\|^{2}$	$w_{\text{ori}}$
$p_{\tau}$	$\\|\boldsymbol{\tau}\\|^{2}$	$w_{\tau}$

Appendix

Table 11: Reward terms used in our MorFiC locomotion objective.

w_{k}

are set in the reward configuration; fixed scalings appearing in code (e.g., the factor 4 in

r_{\text{lin}}

) are shown explicitly.

Target	URMA $v_{x}^{\max}{\pm}\sigma/S$	BodyTrans. $v_{x}^{\max}{\pm}\sigma/S$	GenLoco $v_{x}^{\max}{\pm}\sigma/S$	Embod. $v_{x}^{\max}{\pm}\sigma/S$	MorFiC-F $v_{x}^{\max}{\pm}\sigma/S$
Go2	$2.389{\pm}0.405/\mathbf{1.000}$	$0.313{\pm}0.232/0.625$	$0.592{\pm}0.047/0.922$	$1.072{\pm}0.092/0.859$	$\mathbf{2.405{\pm}0.405}/0.859$
Go1	$\mathbf{2.514{\pm}0.430}/\mathbf{1.000}$	$0.206{\pm}0.151/\mathbf{1.000}$	$0.985{\pm}0.007/\mathbf{1.000}$	$2.343{\pm}0.131/0.797$	$1.972{\pm}0.442/0.516$
A1	$\mathbf{2.230{\pm}0.336}/\mathbf{1.000}$	$0.374{\pm}0.183/0.515$	$0.919{\pm}0.011/\mathbf{1.000}$	$2.143{\pm}0.116/0.719$	$1.595{\pm}0.467/0.156$
AlienGo	$-/0.000$	$0.358{\pm}0.315/0.203$	$\mathbf{0.964{\pm}0.032}/\mathbf{1.000}$	$0.452{\pm}0.085/0.000$	$0.832{\pm}0.542/\mathbf{1.000}$
B1	$-/0.000$	$0.080{\pm}0.140/0.640$	$0.00/0.000$	$\mathbf{3.062{\pm}0.214}/\mathbf{0.797}$	$0.121{\pm}0.060/0.000$
Cheetah	$-/0.000$	$-/\mathbf{1.000}$	$0.729{\pm}0.061/0.969$	$-0.118{\pm}0.091/0.000$	$\mathbf{1.128{\pm}0.986}/0.234$

Appendix

Table 12: External baselines vs. MorFiC at higher commanded speed. Each entry reports

v_{x}^{\max}\pm\sigma/S

(m/s; survival). All methods are evaluated at

v_{x}^{\mathrm{cmd}}=2.5

m/s, except GenLoco, which does not take a commanded forward velocity as input. Bold indicates the best value for each metric independently.

Target	Vanilla PPO $\|\mathrm{NVB}\|$ /NVE/ASA	Concat- $z$ Actor only	Concat- $z$ Actor+Critic	FiLM $\|\mathrm{NVB}\|$ /NVE/ASA
Go2	$1.944/1.981/0.610$	$\mathbf{0.177}/1.168/0.689$	$0.535/\mathbf{0.960}/{0.670}$	$1.768/1.943/\textbf{0.771}$
Go1	$1.591/1.817/0.612$	$\mathbf{0.068}/\mathbf{1.096}/0.662$	$1.623/1.834/0.674$	$1.375/1.653/\mathbf{0.681}$
A1	$2.027/2.203/0.603$	$2.033/16.463/\mathbf{0.754}$	$\mathbf{0.199}/\mathbf{0.936}/0.701$	$1.482/1.813/0.675$
AlienGo	${0.070}/1.454/0.612$	$0.468/1.209/0.569$	$0.153/1.117/0.607$	$\textbf{0.048}/\mathbf{0.835}/\mathbf{0.706}$
B1	$0.182/1.231/0.618$	$0.358/1.187/0.570$	$\mathbf{0.040}/{1.134}/\mathbf{0.624}$	$0.645/\textbf{1.279}/0.618$
Cheetah	$0.362/1.869/0.428$	$\mathbf{0.220}/1.086/0.638$	$1.085/1.344/0.730$	$0.464/\mathbf{0.947}/\mathbf{0.768}$

Appendix

Table 13: Extended critic calibration diagnostics across PPO variants. Each entry reports

|\mathrm{NVB}|

/NVE/ASA, where NVB is the normalized value bias, NVE is the normalized value error, and ASA is the advantage-sign agreement. Lower

|\mathrm{NVB}|

and NVE are better, while higher ASA is better. Best value for each metric within a target row is bolded.

Target	Embod. Scale $\|\mathrm{NVB}\|$ /NVE/ASA	URMA $\|\mathrm{NVB}\|$ /NVE/ASA	BodyTrans. $\|\mathrm{NVB}\|$ /NVE/ASA	GenLoco $\|\mathrm{NVB}\|$ /NVE/ASA	MorFiC-F $\|\mathrm{NVB}\|$ /NVE/ASA
Go2	$3.437/3.646/0.657$	$3.005/3.178/\mathbf{0.702}$	$3.319/3.492/0.652$	$5.458/5.674/0.561$	$\mathbf{1.768}/\mathbf{1.943}/0.671$
Go1	$2.569/2.772/0.607$	$3.170/3.333/0.692$	$4.771/4.983/\mathbf{0.724}$	$3.402/3.594/0.623$	$\mathbf{1.375}/\mathbf{1.653}/0.681$
A1	$2.368/2.585/0.599$	$3.390/3.551/\mathbf{0.686}$	$3.853/4.032/0.686$	$2.956/3.128/0.612$	$\mathbf{1.482}/\mathbf{1.813}/0.675$
AlienGo	–	–	$3.104/3.476/0.661$	$1.170/1.522/\mathbf{0.709}$	$\mathbf{0.098}/\mathbf{0.835}/0.706$
B1	$3.330/3.590/0.657$	–	$3.571/3.781/\mathbf{0.694}$	$7.428/7.729/0.667$	$\mathbf{0.645}/\mathbf{1.279}/0.618$
Cheetah	–	–	–	$5.294/5.511/0.594$	$\mathbf{0.464}/\mathbf{0.947}/\mathbf{0.768}$

Appendix

Table 14: Extended critic calibration diagnostics for external baselines. Each entry reports

|\mathrm{NVB}|

/NVE/ASA, where NVB is normalized value bias, NVE is normalized value error, and ASA is advantage-sign agreement. Lower

|\mathrm{NVB}|

and NVE are better, while higher ASA is better. Best value for each metric within a target row is bolded.

Src.	Go2		Go1		A1		AlienGo		B1		Cheetah		ANYmal-C
	Flip	Cos.	Flip	Cos.	Flip	Cos.	Flip	Cos.	Flip	Cos.	Flip	Cos.	Flip	Cos.
MC	0.000	1.000	0.000	1.000	0.000	1.000	0.000	1.000	0.000	1.000	0.000	1.000	0.000	1.000
MorFiC	0.227	0.880	0.187	0.972	0.239	0.785	0.255	0.366	0.272	-0.182	0.209	0.679	0.402	-0.149
Concat	0.307	0.720	0.151	0.830	0.344	0.427	0.329	0.004	0.269	0.106	0.236	0.575	0.479	-0.419
Act-only	0.524	0.890	0.502	0.924	0.511	0.717	0.318	0.342	0.565	0.647	0.265	0.644	0.470	-0.044
Vanilla PPO	0.235	0.865	0.229	0.684	0.260	0.653	0.322	-0.113	0.176	0.601	0.253	0.264	0.461	-0.074

Appendix

Table 15: Fixed-rollout critic diagnostic across target morphologies. Each entry reports Flip/Cos., where Flip is the sign-flip rate against the MC reference advantage (lower is better) and Cos. is the actor-gradient cosine with the MC-reference gradient (higher is better). Bold indicates the best learned method for each metric independently; the MC row is the reference and is not considered for bolding.

Method	Transitions	Iters.	Sec/iter	GPU-h	GPU-h @400M	Notes
MorFiC	400M	4,000	1.98–2.70	2.2–3.0	2.2–3.0	Single generalist policy; local run
BodyTransformer	400M	8,000	17.25	38.3	39.0	Reproduced model_8000
URMA	1.600B	3,064	366–392	311–333	77.8–83.3	Original training budget
GenLoco	200M	1,526	125.8	53.3	106.6	200M setting
GenLoco	800M	6,104	125.8	213.5	106.8	800M setting
Expert-pool / selected-expert methods

Appendix

Table 16: Training compute comparison. We report total transitions, approximate PPO iterations, wall-clock seconds per iteration, total single-GPU-equivalent training hours, and GPU-hours normalized to a 400M-transition budget. Lower GPU-hours@400M indicates lower compute cost per transition. Expert-pool methods are separated because they train many specialized policies rather than one generalist policy.

Panel of Figure 5 — Figure 5: Above figure shows representative reward and value trajectories during deployment on the Go1 robot. The MorFiC produces smooth value estimates (orange) (second row) that track the expected discounted returns from noisy instantaneous rewards (green). While non-MorFic value estimates are noisy (first row), MorFiC’s morphology-conditioned critic maintains stable value predictions even on unseen morphologies.

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