Humanoid Mobility via Attention-based Contacts

Junzhe He; Kehan Wen; Chong Zhang; Clemens Schwarke; Zewei Zhang; Kaixian Qu; Siyuan Hu; Matthias Müller

Figure 1: Agile and robust humanoid mobility in diverse environments. Our holistic controller enables a humanoid robot (the Unitree G1) to dynamically traverse diverse and challenging environments, including (a) ladder climbing, (b,j) stage climbing, (c) crawling, (d) vaulting over thin walls, (e) stair climbing, (f) standing up from the ground, (g) jumping down, (h) walking over stepping stones, and (i) sitting down, using a single generalist policy.

Figure 2: Overview, part I. (A) Inference-time pipeline. (B) Stage 1: whole-body controller pretraining. Reference trajectories are sampled from the dataset. Training follows a backward curriculum: the robot is initialized at progressively earlier states along the reference trajectory, advancing to an earlier state only after the current one has been successfully learned.

R_{P},R_{R},R_{v},R_{\omega}

,

R_{C}

,

R_{j,p}

, and

R_{j,v}

denote the position, rotation, linear velocity, angular velocity, contact, joint position, and joint velocity tracking reward, respectively. (C) Stage 2: attention-based contact planner. The planner predicts contact plans by attending to map observations, conditioned on robot proprioception and the goal command. It is trained in a supervised manner using ground-truth contact labels from a motion buffer containing rollout trajectories generated by the whole-body controller. The tracker is co-trained using the predicted contacts from the planner.

Figure 3: Overview, part II. Stage 3: RL fine-tuning. Training combines reference tracking on motions sampled from the demonstration dataset (left) with goal-reaching rollouts on procedurally generated terrains outside the demonstration distribution (right). In the goal-reaching environment, the contact planner predicts contact plans from map scans, robot proprioception, and the goal command; the whole-body controller executes these plans and is fine-tuned with RL using task (

R_{t}

) and contact-tracking (

R_{C}

) rewards. Successful rollouts are stored in the fine-tuning buffer and subsequently used as additional supervision for the contact planner, forming a bootstrapping loop in which planner-generated contacts are executed, validated through successful interaction, and recycled to improve the planner. Reference trajectories are sampled proportionally from the original dataset during fine-tuning to retain the previously learned tracking behaviors.

Figure 4: Compositional whole-body motion control. (a) Walking - ladder climbing - jumping down. (b) Walking - stairs climbing - jumping down. (c) Stairs climbing up - stepping stones - stairs climbing down. (d) Stairs climbing up - stairs climbing down - box climbing up - jumping down. (e) Walking - vaulting - box climbing up. (f) Stairs climbing up - beam - jumping down. All motions deployed with a single generalist policy.

Figure 5: Simulation results. The red dots indicate contact plans; the sphere and arrow indicate goal position and orientation. (A) The robot selects different interaction strategies on the same type of terrain depending on the desired goal position and orientation. (B) The fine-tuned policy generalizes to composite terrains and unseen terrains.

Figure 6: Failure recovery. Our generalist controller enabled failure recovery behaviors including but not limited to: (A) re-attempting to stand up if failed due to uneven ground, (B) and (C) standing up after falling down, and (D) recovering from failures (e.g., knee stuck, slipped down from a rung, etc)

Figure 7: Simulation-based evaluations. (A) Stage-1 trackers using contacts alone or contacts plus reference kinematics. (B) Attention and MLP systems under three configurations: Stage 2, a frozen Stage-2 planner paired with a Stage-3 tracker, and the fully fine-tuned Stage-3 system. Bars show mean success, with terrain categories weighted equally. (C) Attention-based systems before and after RL fine-tuning. (D) Attention versus MLP after fine-tuning. In C and D, the upper plots show success rates and the lower plots show contact placement errors; foot and whole denote foot-only and whole-body support. (E) Comparison with MGMT [ 61 ] across terrain categories, individual sparse terrains, and eight composite courses. Each radar axis uses 1,000 episodes per method. The images compare predictions from the same robot state: red markers indicate our contact targets, while MGMT’s predicted foot and hand positions progress from green (earlier) to red (later). Whiskers and shaded bands show 95% confidence intervals.

Capability	PHP [ 49 ]	LLP [ 3 ]	Ours
Sparse footholds	N/A	$\checkmark$	$\checkmark$
Dense footholds	N/A	$\checkmark$	$\checkmark$
Sparse whole-body	N/A	N/A	$\checkmark$
Dense whole-body	$\checkmark$	$\checkmark$	$\checkmark$
Terrain composition	N/A	limited	$\checkmark$
No manual data augmentation	✗	✗	$\checkmark$

Table 1: Qualitative comparison of whole-body locomotion methods.

\checkmark

: demonstrated; N/A: not demonstrated or evaluated.

Figure 8: Overview of the LiDAR-based neural mapping pipeline for height map observations. (A) At each frame, LiDAR points are projected into x-y grid cells and the highest point per cell is retained, producing a 2D local grid map. A neural network then predicts local elevations with associated uncertainty, and the predictions are fused into the global map using odometry. (B) The network uses CNNs to predict per-grid logits over three fill modes: the exact measured value, the neighborhood average, or leaving the grid empty. The mode with the highest logit determines the grid’s elevation prediction, while the disagreement among modes and logits yields the uncertainty estimate. (C) The network is trained on synthetic data generated from diverse scene meshes.

$\mathbf{r}_{b},\mathbf{v}_{b},\boldsymbol{\omega}_{b}$	base position, linear and angular velocity
$\theta_{e}$	angular difference between actual and reference base orientations
$\mathbf{q}_{j},\dot{\mathbf{q}}_{j}$	joint position and velocity ( 0 : default)
$\boldsymbol{\tau}_{j}$	joint torque
$\mathbf{a}_{t}$	action at control step $t$
$(\cdot)^{*}$	supervision target, defined by context
$\hat{\mathbf{p}}_{b},\hat{c}_{b}$	planner-predicted contact position and occupancy probability

Table 2: Nomenclature. Reward kernel bandwidths

\sigma_{(\cdot)}

and other hyperparameter values are introduced inline where used.

Category	Term	Functional Form	Stage 1	Stage 2	Stage 3
Task	track_base_pos	$\exp\!\left(-\chi_{\mathrm{mov}}\\|\mathbf{r}_{b}-\mathbf{r}_{b}^{*}\\|^{2}/\sigma_{p}^{2}-\theta_{e}^{2}/\sigma_{r}^{2}\right)$	$3.0$	$3.0$	$3.0$
	track_base_vel	$\exp\!\left(-\\|\mathbf{v}_{b}-\mathbf{v}_{b}^{}\\|^{2}/\sigma_{v}^{2}-\\|\boldsymbol{\omega}_{b}-\boldsymbol{\omega}_{b}^{}\\|^{2}/\sigma_{\omega}^{2}\right)$	$1.0$	$1.0$	$1.0$
	track_joint_pos	$\exp\!\left(-\\|\operatorname{wrap}_{\pi}(\mathbf{q}_{j}-\mathbf{q}_{j}^{*})\\|^{2}/\sigma_{q}^{2}\right)$	$2.5$	$2.5$	$2.5$
	track_joint_vel	$\exp\!\left(-\\|\dot{\mathbf{q}}_{j}-\dot{\mathbf{q}}_{j}^{*}\\|^{2}/\sigma_{\dot{q}}^{2}\right)$	$0.5$	$0.5$	$0.5$
	track_contact_label	$\frac{1}{9}\sum_{b}c_{b}^{\mathrm{meas}}(2c_{b}^{\mathrm{ref}}-1)$	$5.0$	$5.0(1-\eta_{\mathrm{rew}})$
	track_contact_pos_base	$\exp\!\left(-\sum_{b}\\|\mathbf{p}_{b}^{\mathrm{exec},B}-\mathbf{p}_{b}^{\mathrm{ref},B}\\|^{2}/\sigma_{c}^{2}\right)$	$2.0$	$2.0(1-\eta_{\mathrm{rew}})$

Table 3: Definition of reward terms across training stages. The per-step reward is

\Delta t\sum_{i}w_{i}r_{i}

, where

\Delta t

is the control timestep and

w_{i}

are the weights listed below. Grey cells denote inactive terms. Reference-tracking terms apply only to reference-anchored environments; terms marked † apply only to goal-reaching environments. The Stage 2 contact weights use

\eta_{\mathrm{rew}}=\eta_{\mathrm{rew}}(u)

, the reward-annealing coefficient defined in ( 3 ). The index

b

runs over the nine contact bodies,

j

over the 23 controlled joints, and

f

over monitored contact-sensor links. Superscripts

\mathrm{ref}

denote instantaneous reference quantities;

B

and

W

denote body-yaw and world coordinates. Actual and reference body-yaw positions use their respective base poses.

\theta_{e}

is the angular difference between actual and reference base orientations,

\chi_{\mathrm{mov}}=\mathds{1}[\|\mathbf{v}_{b}^{*}\|>0.1]

, and

m_{b}

indicates a nonzero, occupancy-gated planner target.

c_{b}^{\mathrm{meas}}

indicates a vertical contact-force magnitude exceeding

1\,\mathrm{N}

within the sensor-history window.

\operatorname{wrap}_{\pi}

wraps angular differences to

[-\pi,\pi)

. The kernel scales are

\sigma_{p}=0.5

,

\sigma_{r}=1

,

\sigma_{v}=1

,

\sigma_{\omega}=3

,

\sigma_{q}=2

,

\sigma_{\dot{q}}=10

, and

\sigma_{c}=1

, in the corresponding SI units. For goal rewards,

g_{xy}=\mathds{1}[d_{g}<0.5]

,

g_{h}=\mathds{1}[|\Delta z|<0.2]

,

g_{\psi}=\mathds{1}[|\Delta\psi|<0.5]

, and

g_{v}=\mathds{1}[v_{\to g}>0.1]\mathds{1}[\|\mathbf{v}_{b,xy}^{W}\|\leq v_{\max}]

. Here,

d_{g}

is the horizontal goal distance,

\Delta z

is the target base height minus the current base height,

\Delta\psi

is the target-heading error, and

v_{\to g}

is the horizontal velocity projected toward the goal. The speed cap is

0.8\,\mathrm{m\,s^{-1}}

on the configured stair terrains and

2.0\,\mathrm{m\,s^{-1}}

elsewhere. For get-up terrains,

g_{z}=\mathds{1}[v_{b,z}^{W}\operatorname{sign}(\Delta z)>0.1\lor|\Delta z|<0.2]

; otherwise,

g_{z}=1

.

d_{\mathrm{foot}}

is the fraction of feet without measured contact,

d_{\mathrm{tilt}}=1-(g_{z}^{\mathrm{base}})^{2}

uses the vertical component of projected gravity, and

d_{q}=\frac{1}{23}\sum_{j}|q_{j}-q_{0,j}|

.

T_{i}

denotes the terrain mask for style term

i

.

F_{f,xy}^{\max}

and

F_{f,z}^{\max}

are the maximum horizontal force magnitude and vertical force over the sensor-history window;

t_{f}^{\mathrm{contact}}

is the continuous contact duration.

\mathbf{g}_{\mathrm{torso}}

is gravity projected into the torso frame. Computed and applied torques are taken before and after actuator limiting, respectively.

[x]_{+}=\max(x,0)

, and joint bounds are the configured soft limits. All thresholds use SI units.

	Data origin	Retargeted	Contact labeled
Box climbing	Omniretarget [ 54 ]	No	Yes
Stairs climbing	Mixamo [ 31 ]	Yes	Yes
Ladder climbing	Mixamo [ 31 ]	Yes	Yes
Sit down	Mixamo [ 31 ]	Yes	Yes
Walk	LAFAN [ 11 ]	Yes	Yes
Get up	LAFAN [ 11 ]	Yes	Yes

Table S1 : Source of the motion data. Retargeted: retargeted using our method; Contact labeled: contact labeled with our method.

Parameter	Value
Dynamics
Contact friction (static/dynamic)	$\mathcal{U}(0.3,1.2)$ / $\mathcal{U}(0.3,1.2)$ ; ground friction $=1.0$
Restitution	$\mathcal{U}(0.0,0.5)$
Torso added mass	$\mathcal{U}(-2.0,4.0)\,\mathrm{kg}$
Leg link mass	$\times\mathcal{U}(0.85,1.15)$
Torso CoM offset	$x:\pm 0.025\,\mathrm{m}$ , $y,z:\pm 0.05\,\mathrm{m}$

Table S2 : Domain randomization settings.

\mathcal{U}(a,b)

denotes a uniform distribution over

[a,b]

. Multiplicative factors are applied to nominal values. Dynamics parameters are sampled once per environment at simulation start.

Component	Dimensions	Details
Attention planner (786,993 parameters)
Terrain-point embedding	$3\rightarrow 16$	Linear projection; ELU
Height-map encoder	$1\rightarrow 16\rightarrow 48$	$5\times 5$ kernels; padding 2; ELU
Terrain-feature projection	$64\rightarrow 96$	Linear projection
Terrain-context encoder	$96\rightarrow 64\rightarrow 64$	Pointwise MLP; max pooling
Proprioception–goal–context encoder	$442\rightarrow 128\rightarrow 128\rightarrow 96$	MLP; ReLU

Table S3 : Contact-planner architectures. Both planners receive a five-step proprioceptive history, a three-dimensional goal command, and 187 terrain points. Arrows indicate layer widths; height-map encoder widths denote channels.

Observation encoding
Parameter	Value
Proprioceptive history	5 control steps
Height-scan spacing	$0.1\,\mathrm{m}$
Planner scan coverage	$1.6\times 1.0\,\mathrm{m}$
Tracker scan coverage	$0.8\times 0.6\,\mathrm{m}$
Reference-goal lookahead	$0.5$ – $1.5\,\mathrm{s}$

Table S4 : Observation and curriculum settings. Reference phases are fractions of the motion-clip duration. Horizontal curriculum distances are measured only when the vertical goal error is below

0.1\,\mathrm{m}

.

Optimization and decoding
Parameter	Value
Optimizer	Adam
Planner learning rate	$10^{-4}$
Adam $(\beta_{1},\beta_{2})$	$(0.9,0.999)$
Adam $\epsilon$	$10^{-8}$
Weight decay	$0$

Table S5 : Planner optimization and hindsight-labeling settings. Contact duration and trajectory length are measured in

50\,\mathrm{Hz}

control steps. The trajectory-storage limit is separate from the environment’s episode timeout.

Rollout and batch sizes
Parameter	Stage 1	Stage 2	Stage 3
Parallel environments per worker	$12{,}000$	$2{,}400$	$2{,}100$
Rollout batch per worker	$288{,}000$	$57{,}600$	$50{,}400$
Minibatch per worker	$36{,}000$	$7{,}200$	$6{,}300$
Training workers (one GPU each)	—	$2$	$4$
Total parallel environments	—	$4{,}800$	$8{,}400$

Table S6 : PPO optimization settings. Batch sizes count transitions. Per-worker minibatches are one eighth of the corresponding rollout batch; effective total minibatches include all workers. Stage-1 distributed totals are not reported.

Figure S1 : Eight curated composite courses used for evaluation. Each panel shows four successive robot poses from one successful traversal. Green markers indicate starting positions, and red circles show the 0.5 m horizontal goal tolerance. Success rates for Ours and MGMT are measured over 1,000 episodes per method and course.

Humanoid Mobility via Attention-based Contacts

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