Articulated-Body Dynamics Network: Dynamics-Grounded Prior for Robot Learning

Sangwoo Shin; Kunzhao Ren; Xiaobin Xiong; Josiah P. Hanna

cs.ROMar 19, 2026

Articulated-Body Dynamics Network: Dynamics-Grounded Prior for Robot Learning

Authors: Sangwoo Shin, Kunzhao Ren, Xiaobin Xiong, Josiah P. Hanna

Organizations: University of Wisconsin–Madison. · Shanghai Innovation Institute (SII).

Abstract

Recent work in reinforcement learning has shown that incorporating structural priors for articulated robots, such as link connectivity, into policy networks improves learning efficiency. However, dynamics properties, despite their fundamental role in determining how forces and motion propagate through the body, remain largely underexplored as an inductive bias for policy learning. To address this gap, we present the Articulated-Body Dynamics Network (ABD-Net), a novel graph neural network architecture grounded in the computational structure of forward dynamics. Specifically, we adapt the inertia propagation mechanism from the Articulated Body Algorithm, systematically aggregating inertial quantities from child to parent links in a tree-structured manner, while replacing physical quantities with learnable parameters. Embedding ABD-NET into the policy actor enables dynamics-informed representations that capture how actions propagate through the body, leading to efficient and robust policy learning. Through experiments with simulated humanoid, quadruped, and hopper robots, our approach demonstrates increased sample efficiency and generalization to dynamics shifts compared to transformer-based and GNN baselines. We further validate the learned policy on real Unitree G1 and Go2 robots, state-of-the-art humanoid and quadruped platforms, generating dynamic, versatile and robust locomotion behaviors through sim-to-real transfer with real-time inference.

Figures & tables

Fig. 1: Different approaches to computing node features for articulated robots. Conventional methods use link connectivity to define information flow via adjacency or attention mask, leaving the network to learn how to form node features from scratch. Our approach encodes the computational structure of forward dynamics by performing dynamics-inspired message passing, where learnable inertia-related quantities (denoted as $I^{a}$ ) are propagated and aggregated from children to parents to form node features.

Fig. 2: Overview of ABD-Net on a quadruped robot. (a) Observation Encoding: Each link $i$ has its own projection $\phi_{i}$ that transforms the observation $\mathbf{s}$ into a link-wise observation embedding $\mathbf{z}_{i}$ (e.g., FR-Thigh, FR-Calf, FR-Foot for the front-right leg). (b) Dynamics-Informed Message Passing: Each link $i$ is associated with learnable parameters $(\mathbf{W}_{i},\mathbf{B}_{i})$ . Link $j$ computes a contribution $\mathbf{v}^{a}_{j}$ using $\mathbf{W}_{j}$ and sends it to its parent, which aggregates contributions from all children to form its link representation $\mathbf{v}_{i}$ ( $\sigma$ denotes softplus). (c) Action Decoding: For joint $j$ connecting $\textsc{pa}(j)$ and link $j$ , the action $\mathbf{a}_{j}$ is computed from the parent’s representation $\mathbf{v}_{\textsc{pa}(j)}$ .

Fig. 3: Learning curves comparing ABD-Net (ours) and baselines: mean return versus the number of environment steps. All methods are trained with 5 seeds. Shaded regions indicate 95% standard confidence intervals.

Category	Reward Term	Go1	Go2	G1	T1
Vel. Track.	Lin. vel. tracking	1.5	1.0	1.0	1.0
Vel. Track.	Ang. vel. tracking	0.75	0.2	0.5	0.5
Base Reg.	Base height	12.5	50.0	10.0	20.0
	Vertical lin. vel. ( $\downarrow$ )	2.0	1.0	2.0	1.0
	Ang. vel. xy ( $\downarrow$ )	0.025	–	0.05	0.025
Joint Reg.	Action rate ( $\downarrow$ )	0.02	0.005	0.01	0.1

TABLE I: Reward functions and weights for Genesis environments. (

\downarrow

) denotes penalty terms.

Genesis (T1 + G1 + Go1 + Go2)
Method	IQM	Median	Mean
ABD-Net	0.85 (0.73, 0.95)	0.86 (0.70, 0.97)	0.83 (0.75, 0.91)
BoT	0.69 (0.56, 0.85)	0.67 (0.54, 0.93)	0.70 (0.58, 0.82)
SWAT	0.79 (0.50, 0.94)	0.83 (0.39, 0.95)	0.75 (0.57, 0.89)
Rodrigues	0.45 (0.17, 0.71)	0.45 (0.04, 0.81)	0.45 (0.25, 0.65)
GNN	0.76 (0.65, 0.85)	0.76 (0.65, 0.87)	0.74 (0.67, 0.82)

TABLE II: Normalized final performance on Genesis and SAPIEN.

Algorithm	Humanoid	Hopper	Go2	T1
ABD-Net	91.1 $\pm$ 1.4	62.4 $\pm$ 0.5	82.4 $\pm$ 2.1	81.1 $\pm$ 3.5
BoT	17.0 $\pm$ 0.6	N/C	69.7 $\pm$ 2.3	57.0 $\pm$ 2.1
SWAT	88.9 $\pm$ 2.0	29.7 $\pm$ 1.0	81.4 $\pm$ 2.2	53.4 $\pm$ 1.6
Rodrigues	28.0 $\pm$ 1.7	9.1 $\pm$ 0.4	53.7 $\pm$ 3.1	N/C
GNN	54.9 $\pm$ 0.8	N/C	82.9 $\pm$ 2.2	69.9 $\pm$ 2.4
MLP	78.4 $\pm$ 2.9	55.4 $\pm$ 2.1	66.5 $\pm$ 2.7	N/C

TABLE III: Mass generalization performance (Retention, %). N/C indicates that the training policy did not converge.

Fig. 4: Recovery behavior under 2 $\times$ mass on Hopper Hop. Top: ABD-Net applies stronger torque to recover from the downward tilt. Bottom: SWAT fails to compensate and falls.

Fig. 5: Learned link representations on Go2 during trot gait. Left: Feature norm time series of hip joints (FL: front-left, RR: rear-right, etc.). Right: Correlation rank matrix between hip joint features, where lower rank indicates higher correlation.

Fig. 6: Comparison of ABD-Net and MLP as dynamics models. Left: Single-step validation loss on Double Pendulum and Hopper. Right: 1, 3, 5-step rollout prediction error.

Fig. 7: Learning curves comparing ABD-Net , ABD-Net w/o orth., and GNN across four tasks

Algorithm	Humanoid	Hopper	Go2	T1
ABD-Net	91.1 $\pm$ 1.4	62.4 $\pm$ 0.5	96.2 $\pm$ 0.6	81.1 $\pm$ 3.5
w/o orth.	59.8 $\pm$ 0.4	56.3 $\pm$ 0.8	77.4 $\pm$ 2.2	51.6 $\pm$ 2.2
GNN	54.9 $\pm$ 0.8	N/C	82.9 $\pm$ 2.2	69.9 $\pm$ 2.4

TABLE IV: Mass generalization performance

Fig. 8: Sim-to-real transfer on Unitree Go2 and G1 robots. Top two rows: Go2 velocity tracking across diverse terrains (packed dirt, asphalt, grass, indoor tile), with composite motion sequences showing lateral walking on grass and yaw tracking on indoor tile. Bottom: G1 velocity tracking with composite motion sequences showing forward and lateral walking (left) and motion tracking of a dance sequence (right).

Fig. 9: Effect of observation history length on G1. ABD-Net and MLP are compared across history lengths $\in\{1,3,8,16\}$ .

Fig. 10: Left: FLOPs per forward pass. Right: Inference time. All measured on an RTX 4090 with batch size 2048.

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Learning Smooth Time-Varying Linear Policies with an Action Jacobian Penalty

Zhaoming Xie, Kevin Karol, Jessica Hodgins

Robotics AI Institute, Cambridge, Massachusetts, USA

RL Control Robot Imitation Learning Jacobian Regularization

Open paper AskPDF arXiv

Reinforcement learning provides a framework for learning control policies that can reproduce diverse motions for simulated characters. However, such policies often exploit unnatural high-frequency signals that are unachievable by humans or physical robots, making them poor representations of real-world behaviors. Existing work addresses this issue by adding a reward term that penalizes a large change in actions over time. This term often requires substantial tuning efforts. We propose to use the action Jacobian penalty, which penalizes changes in action with respect to the changes in simulated state directly through auto differentiation. This effectively eliminates unrealistic high-frequency control signals without task specific tuning. While effective, the action Jacobian penalty introduces significant computational overhead when used with traditional fully connected neural network architectures. To mitigate this, we introduce a new architecture called a Linear Policy Net (LPN) that significantly reduces the computational burden for calculating the action Jacobian penalty during training. In addition, a LPN requires no parameter tuning, exhibits faster learning convergence compared to baseline methods, and can be more efficiently queried during inference time compared to a fully connected neural network. We demonstrate that a Linear Policy Net, combined with the action Jacobian penalty, is able to learn policies that generate smooth signals while solving a number of motion imitation tasks with different characteristics, including dynamic motions such as a backflip and various challenging parkour skills. Finally, we apply this approach to create policies for dynamic motions on a physical quadrupedal robot equipped with an arm.

Abstract

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