Humanoid robots are envisioned to perform diverse human-level tasks through their anthropomorphic morphology. Their dual-arm configuration enables a broad range of everyday actions. Yet, as in humans, this morphology can constrain loco-manipulation when both arms are occupied or additional contacts are required beyond their reach. Supernumerary robotic limbs (SRLs) offer a way to extend these capabilities, but their integration requires the added limb to be coordinated with whole-body motion and balance. In this study, we develop and integrate a supernumerary arm into a humanoid platform to investigate how morphological augmentation reshapes its feasible action space. Through quantitative analysis and hardware experiments across two configurations, we show how the additional limb expands whole-body interaction capabilities by enabling manipulation and support to be coordinated beyond the constraints of the native dual-arm configuration. To control this augmented morphology, we leverage model-based trajectory optimization (TO) to generate dynamically feasible motions for goal-conditioned reinforcement learning (RL) controllers. The controllers are trained in simulation and transferred to hardware in a zero-shot manner, enabling coordinated whole-body skills for contact-rich tri-arm loco-manipulation. We further show vision-guided autonomous execution on selected tasks using diffusion policies trained from hardware demonstrations. Our findings suggest that humanoid morphology need not be restricted to human-like forms, but can be reimagined as an extensible design space for robotic augmentation.
Figures & tables
Figure 1: Configurations and real world tasks. The humanoid platform is equipped with a supernumerary 4 -DoF arm in neck-mounted and back-mounted embodiments. (A–G) Photographs of both configurations in distinct SRL poses. (H–T) Task snapshots illustrating the diversity of behaviors enabled by the tri-arm morphology, including reach-augmented manipulation, coordinated manipulation, dynamic loco-manipulation, and human–robot collaborative whole-body behaviors.
Figure 2: Morphological augmentation of workspace and support. ( A ) Neck-mounted and back-mounted SRL embodiments. ( B ) Workspace augmentation in body-frame. ( i ) Reachable workspace overlays for the native arms only, native arms with neck-mounted SRL, and native arms with back-mounted SRL. ( ii ) Directional reach comparison in the body frame (F: forward; R: rearward; LL: left lateral; LR: right lateral; U: upward; D: downward). ( iii ) Workspace decomposition into single-arm volume, dual-arm co-reach, and tri-arm co-reach. ( C ) Translational manipulability isotropy across nominal standing frame slices. The neck-mounted SRL enhances manipulability in frontal and overhead regions, whereas the back-mounted SRL improves performance in the rear, lateral, and lower regions. ( D ) Projected CoM distributions for sampled SRL configurations and payloads of 0−4 kg, compared with the foot-contact polygons of the selected standing configurations.
Figure 3: Support and active stability augmentation with the SRL. ( A, B ) CAREN perturbation experiments with and without back-mounted SRL support against the external frame. ( C ) Forward leaning while the native arms carry a payload and the SRL presses against a wall. ( D, E ) CoM responses with SRL support under repeated 10 cm perturbations and without support under increasing perturbation amplitudes, including balance loss at 7.5 cm. The 10 cm amplitude is the experimental safety limit. ( F ) Analysis of wall bracing. ( i ) Global-frame CoM and SRL-endpoint trajectories relative to the feet midpoint. The feet-only support polygon and projected contact hull are shown separately from conditional static-equilibrium regions computed with unilateral contacts, wall and floor friction coefficients μ=1 , and wall-normal-force caps of 5% , 10% , and 20% of modeled weight W . ( ii ) Forward CoM position versus time, showing a peak excursion of 16.1 cm beyond the feet-only forward boundary.
Figure 4: Reach-augmented manipulation with the SRL. (A–D) High-shelf retrieval, shelf transfer without torso reorientation, native-arm-supported reach-around, and concurrent rear/front manipulation. (E–H) Corresponding reference-based analyses. (i) Body-frame signed distance to the sampled native-arm workspace; positive values indicate points outside, and shading indicates voxel-size sensitivity ( 15 – 25 mm). (ii) World-frame SRL and torso heights (E) ; initial-heading-frame SRL trajectory between shelves (F) ; projected CoM trajectory and conditional static-support regions (G) ; and instantaneous body-frame SRL and right-hand positions (H) .
Figure 5: Coordinated augmentation through tri-arm manipulation. ( A ) Shelf transfer, in which the native arms lift a box from a low shelf and the SRL assists in final placement on a high shelf. ( B ) Coordinated loading, in which the native arms lift a container while the SRL retrieves an object from a top shelf and places it into the container. ( C ) Stacked-box stabilization, in which the native arms lift a multi-layer box stack while the SRL provides an additional stabilizing contact. ( D )( i ) The vertical motion of the SRL and native left hand in the instantaneous body frame during during shelf transfer. ( D )( ii ) The full object path to the final high-shelf placement. ( E ) The heights of the SRL and native left hand in the instantaneous body frame during coordinated loading. ( F ) Contact schematic and Ferrari–Canny sensitivity analysis for stacked-box stabilization, showing that the added SRL contact increases wrench support and enlarges the region of positive ϵ values under a frictional contact model.
Figure 6: Dynamic and collaborative whole-body augmentation with tri-arm coordination. ( A ) Collaborative table transport with a human partner, where the native arms share the table load while the SRL stabilizes a loose object during lifting and walking. ( B ) Box transport through a weighted door, with the native arms maintaining the carried object while the neck-mounted SRL pushes the door during locomotion. ( C ) Door opening with the back-mounted SRL, which engages the handle from behind while the native arms continue carrying a box.
Figure 7: Hierarchical framework for supernumerary humanoid loco-manipulation. Trajectory optimization generates dynamically feasible whole-body references that coordinate the native limbs and SRL under contact and actuation constraints. Learn-to-Teach combines privileged teacher supervision and shared experience to train a student policy for reference tracking using noisy proprioceptive observations. The student policy transfers zero-shot to hardware, enabling coordinated manipulation, support, and locomotion through whole-body feedback control. Vision-guided references extend the same control framework to autonomous task execution.
Figure S1 : Exploded view of the supernumerary arm. . The shoulder comprises three co-located joints, with the actuators housed in high-infill 3D-printed brackets. The elbow link consists of two parallel aluminum plates that provide structural rigidity and accommodate a dual-supported bearing arrangement and belt-tensioning mechanism. The elbow is actuated remotely through a 3:1 belt transmission. The hollow aluminum forearm provides structural stiffness and internal cable routing, with an interface for different end-effectors. The assembly is shown with a parallel-jaw gripper.
Property
Specification
Degrees of freedom / arm length
4 / 83.0 cm
Upper arm / forearm length
37.3 / 45.7 cm
Total mounted mass
4.7 kg
Continuous / peak payload
2 / 4 kg
Gripper mass
0.5 kg
Battery / approximate runtime
36 V, 8 Ah / ∼65 min
Table S1 : SRL system and integration specifications
Joint
Motion
Actuator
External ratio
Continuous torque
Peak torque
Joint range
J1
Shoulder yaw
RS-02
1:1
±6 Nm
±17 Nm
[−180∘,180∘]
J2
Shoulder pitch
RS-03
1:1
±20 Nm
±60 Nm
[−100∘,100∘]
J3
Shoulder roll
RS-02
1:1
±6 Nm
±17 Nm
[−90∘,90∘]
J4
Elbow
RS-02
3:1
±6 Nm
±17 Nm
[−125∘,50∘]
Table S2 : Joint and actuator specifications of the SRL
Component
Material
Fabrication
Detail
Main shoulder bracket
PLA
3D printed
Actuator housing
Primary elbow plate
AL-6061
Waterjet
Elbow structure
Secondary elbow plate
AL-6061
Waterjet
Elbow structure
Elbow shells
PLA
3D printed
Elbow enclosure
Forearm tube
AL-6061
OTS
Internal cable routing
Wrist shaft
AL-7075
Machined
Keyed interface
Table S3 : Mechanical components and fabrication of the SRL
Figure S2 : SRL tracking under different payloads. (A, B) Encoder-derived paths with a 5 lb payload, projected onto the xy plane for the square ( z=0.30 m) and the xz plane for the circle ( y=0.50 m). The square has 0.30 m sides, and the circle has a 0.30 m radius; black dashed curves indicate commanded reference trajectories. Colors denote mean reference speeds of approximately 0.10 , 0.20 , and 0.30 m/s. (C, D) Time-weighted 3D position RMSE versus payload for the square and circle trajectories, respectively. Each point summarizes approximately ten analyzed cycles from a single recording.
Figure S3 : Multi-view visualization of the augmented workspace. Reachable workspaces for the neck-mounted (top row) and back-mounted (bottom row) configurations, displayed from isometric, front, side, and top views. Translucent volumes represent the reachable workspaces of the native arms and the SRLs, illustrating their spatial overlap.
Setting
Value or implementation
Solver
Crocoddyl FDDP
Time integration
Symplectic (semi-implicit) Euler
Time step
Δt=0.005 s
Control parameterization
Piecewise-constant joint torques
Maximum iterations
200 per phase
Solver stopping threshold
10−8
Table S4 : Trajectory-optimization settings for the neck-mounted example
Input
Symbol
Dimension
Student
Teacher
Base Linear Velocity
p˙tb
3
✓
✓
Base Angular Velocity
ωtb
3
✓
✓
Projected Gravity
gt
3
✓
✓
History Motor Joint Position
qhistj
200
✓
✓
Motor Joint Velocity
q˙tj
20
✓
✓
Ref. End-effector Position
p^tee
15
✓
✓
Table S5 : Observation spaces.
Category
Term
Expression
Weight
Task Reward
Motor Joint Position
exp(−5∥q^tj−qtj∥22)
3
Base Position
exp(−20∥p^tb−ptb∥22)
3
Base Orientation
exp(−50∥θ^tb−θtb∥22)
3
Base Linear Velocity
exp(−2∥p˙^tb−p˙tb∥22)
3
Base Angular Velocity
exp(−0.5∥ω^tb−ωtb∥22)
3
End-effector Position
exp(−20∥p^tee−ptee∥22)
3
Table S6 : Reward Components and Weights.
Category
Parameter
Type
Range / Std
Observation
Ref. End-effector Position (m)
Additive Gaussian
σ=0.04
Motor Joint Position (rad)
Additive Gaussian
σ=0.035
Joint Velocity (rad/s)
Additive Gaussian
σ=0.03
Base Linear Velocity (m/s)
Additive Gaussian
σ=0.03
Base Angular Velocity (rad/s)
Additive Gaussian
σ=0.03
Projected gravity direction (unitless)
Gaussian; unit norm
σ=0.015
Table S7 : Domain Randomization Parameters.
Parameter
Value
PPO clipping parameter ϵ
0.3
Discount factor γ
0.97
Learning rate
5×10−5
Entropy coefficient
1×10−2
Rollout length
20
Number of minibatches
32
Table S8 : RL policy training hyperparameters.
Δ vs. Asym-PPO (%)
Metric
Asym-PPO
L2T (ours)
Mean
Max
Episodic return (teacher =1 ) ↑
0.916
0.964
+5.3
+9.1
End-effector MPKPE (mm) ↓
124.1
113.3
+11.2
+32.6
Joint-position RMSE (rad) ↓
0.053
0.048
+8.6
+35.0
Table S9 : Comparison of whole-body controller performance. Both policies use onboard observations. Values are task averages, with episodic return normalized by the privileged teacher for each task. Relative improvements are computed per task and then averaged; positive values indicate higher return or lower tracking error. MPKPE measures end-effector position error in the robot’s base frame. Results use one training seed per task.
Figure S4 : Distribution of controller performance improvements. Relative improvements of the L2T student over Asym-PPO in episodic return, end-effector tracking, and joint-position tracking. Each dot represents an evaluated task, and horizontal bars indicate averages across tasks. Positive values indicate higher return or lower tracking error for L2T; negative values favor Asym-PPO.
Type
Signal
Dim.
Rate
Shelf
Box
Door
Observation
Torso / SRL end-effector RGB-D
240×424×4 each
15 Hz
✓
✓
✓
Motor positions
24
200 Hz
✓
✓
✓
Gripper state (last command)
1
200 Hz
✓
Policy mode (last command)
1
200 Hz
✓
Action
End-effector positions (body frame)
3×5
50 Hz
✓
✓
✓
Base pose (body frame)
6
50 Hz
✓
✓
Table S10 : Diffusion-policy observation and action specifications. Sensor rates are logging rates; training data are resampled to 50 Hz, with each sample paired with the most recent images. Check marks indicate signals used by each task-specific policy: top-shelf retrieval (Shelf), stacked-box stabilization (Box), and object transport during door interaction (Door).
Wearable robots aim to seamlessly adapt to humans and their environment with personalized interactions. Existing supernumerary robotic limbs (SRLs), which enhance the physical capabilities of humans with additional extremities, have thus far been developed primarily for task-specific applications in structured industrial settings, limiting their adaptability to dynamic and unstructured environments. Here, we introduce a novel reconfigurable SRL framework grounded in a quantitative analysis of human augmentation to guide the development of more adaptable SRLs for diverse scenarios. This framework captures how SRL configuration shapes workspace extension and human-robot collaboration. We define human augmentation ratios to evaluate collaborative, visible extended, and non-visible extended workspaces, enabling systematic selection of SRL placement, morphology, and autonomy for a given task. Using these metrics, we demonstrate how quantitative augmentation analysis can guide the reconfiguration and control of SRLs to better match task requirements. We validate the proposed approach through experiments with a reconfigurable SRL composed of origami-inspired modular elements. Our results suggest that reconfigurable SRLs, informed by quantitative human augmentation analysis, offer a new perspective for providing adaptable human augmentation and assistance in everyday environments.
Mustafa Mete, Anastasia Bolotnikova, Alexander Schuessler +1
Reconfigurable Robotics Lab, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland. · Laboratory for Analysis and Architecture of Systems (LAAS), CNRS, Toulouse, France.
Supernumerary robotic limbs (SLs) have the potential to transform a wide range of human activities, yet their usability remains limited by key technical challenges, particularly in ensuring safety and achieving versatile control. Here, we address the critical problem of maintaining balance in the human-SLs system, a prerequisite for safe and comfortable augmentation tasks. Unlike previous approaches that developed SLs specifically for stability support, we propose a general framework for preserving balance with SLs designed for generic use. Our hierarchical three-layer architecture consists of: (i) a prediction layer that estimates human trunk and center of mass (CoM) dynamics, (ii) a planning layer that generates optimal CoM trajectories to counteract trunk movements and computes the corresponding SL control inputs, and (iii) a control layer that executes these inputs on the SL hardware. We evaluated the framework with ten participants performing forward and lateral bending tasks. The results show a clear reduction in stance instability, demonstrating the framework's effectiveness in enhancing balance. This work paves the path towards safe and versatile human-SLs interactions. [This paper has been submitted for publication to IEEE.]
Whole-body humanoid loco-manipulation requires coordinating the robot's entire kinematic chain. However, most existing systems typically decouple the upper and lower bodies into separate controllers, limiting such coordination and yielding behaviors similar to those of a wheeled dual-arm platform. In this paper, we ask what it takes to build a whole-body native vision-language-action (VLA) model that maps language and pixels directly to all of the humanoid's degrees of freedom. We conduct a systematic empirical study organized as a roadmap of one-variable-at-a-time experiments across three phases: whole-body teleoperation, VLA model design, and heterogeneous co-training. Our study yields several intriguing findings: a joint-based whole-body teleoperation interface outperforms alternatives that only partially expose the humanoid's degrees of freedom; a VLA pretrained on static and wheeled dual-arm platforms transfers surprisingly well to a humanoid's full action space; and co-training with HuMI, the humanoid analog of UMI, extends the policy to new objects and instructions without additional whole-body teleoperation on those targets. Following this roadmap yields OpenHLM, an open-source recipe for whole-body humanoid loco-manipulation. In a challenging long-horizon task that spans a wide vertical range of the humanoid, OpenHLM outperforms two state-of-the-art humanoid VLA baselines (GR00T N1.6 and Ψ0) using less than half the total demonstration time. Our code, training data, and model checkpoints are available at [https://openhlm-project.github.io/].
Yingdong Hu, Haodong Zhu, Boyuan Zheng +6
Tsinghua University · Shanghai Qi Zhi Institute · Spirit AI