💻 computer science

Visible-Reachable Workspace for Perception-Aware Humanoid Design

This paper introduces the visible-reachable workspace (VRW) as a perception-aware design metric and demonstrates through a custom 31-DoF humanoid with independently actuated cameras that such articulation significantly expands observable reachability and improves manipulation efficiency compared to fixed-sensor designs.

Original authors: Boxi Xia, Zijiang Yang, Ryan Shin, Bokuan Li, Eric Wun-Hao Lu, Jacob Lee, Jiaxun Liu, Boyuan Chen

Published 2026-09-09

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CC BY 4.0

Original authors: Boxi Xia, Zijiang Yang, Ryan Shin, Bokuan Li, Eric Wun-Hao Lu, Jacob Lee, Jiaxun Liu, Boyuan Chen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

For a robot to pick up an object, it must first be able to reach it with its arm. This simple geometric fact has long been the standard way engineers measure a robot's capability. They calculate the "workspace," or the three-dimensional volume of space where the robot's hand can physically go. However, for a robot that relies on cameras to see what it is doing, reachability is only half the story. A target might be perfectly within the robot's arm's reach, yet completely invisible to its eyes because the robot's body blocks the view, or because its cameras are pointed in the wrong direction. If the robot cannot see the object it is trying to grab, it cannot plan the movement to get it. This creates a frustrating gap: the robot is physically capable of the task but perceptually blind to it, forcing it to waste time and energy repositioning its entire body just to get a glimpse of what it needs.

Researchers at Duke University set out to close this gap by rethinking how robots are built. They introduced a new way of measuring a robot's potential called the "visible-reachable workspace." Instead of just asking where the robot can reach, they asked where it can reach and see at the same time. To test this idea, they built a new humanoid robot, the Duke Humanoid V2, designed specifically to solve the problem of seeing while reaching. Unlike most robots that have fixed cameras in their heads, or cameras that move only when the whole head turns, this robot has two independent cameras mounted on a special gimbal. These cameras can swivel left, right, up, and down on their own, completely separate from the robot's arms and torso. This design allows the robot to look at one object with one camera while its arm reaches for a different object, all without moving its body.

The team used their new measurement to compare this custom robot against several existing humanoid models. They found a significant difference in capability. On the Duke Humanoid V2, the independently moving cameras allowed the robot to see 97 percent of the space its arms could reach. In contrast, when the same cameras were locked in place, the robot could only see 38 percent of that reachable space. Other humanoid robots, even those with moving necks, fared worse. A fixed-head robot could see only 16 percent of its reachable workspace, while robots with necks that could turn managed between 48 and 76 percent. The researchers discovered that simply adding more cameras did not solve the problem as well as making the existing cameras move independently. Adding a second independent camera to the robot increased its ability to watch two separate areas at once from 45 percent to 95 percent. Adding a third camera provided almost no extra benefit, raising the number only to 97 percent, suggesting that two well-placed, moving eyes are far more valuable than three fixed ones.

To prove that this design actually helps the robot work better, the team ran a series of tests where the robot had to find and grab two objects placed in different locations. In some scenarios, the objects were side by side; in others, one was in front and one was behind. They compared the robot with its moving cameras against the same robot with its cameras locked in place. The results were clear: the robot with the moving cameras finished the tasks 17 percent faster and used 19 percent less mechanical energy. The savings came from every stage of the process. The robot with moving eyes spent less time searching for the objects because it could simply turn its cameras to find them, rather than having to walk around or twist its whole body to get a view. It also spent less time walking toward the objects because it could spot them from a distance before moving. Even the actual act of grabbing the objects was faster, as the robot could keep one eye on the target while its arm moved, without needing to stop and reorient itself.

The researchers took these findings from computer simulations into the real world, where the robot successfully performed the same tasks on a physical table. It could watch a target in front of it while reaching for one behind it, or track two people holding objects that moved independently. When an arm blocked the view of a target, the corresponding camera would actively search for it and reacquire it the moment it became visible again. These physical demonstrations confirmed that the design principle works outside of a computer model. The study suggests that for robots to become truly effective at tasks requiring both sight and touch, the design of their sensors must be integrated with the design of their limbs. By treating visibility as a constraint that shapes the robot's physical form, rather than an afterthought, engineers can build machines that move more efficiently and perform complex tasks with greater ease. The team has made the designs and software for this robot available to the public, hoping that others will use these insights to build the next generation of capable, perceptive machines.

Technical Summary: Visible-Reachable Workspace for Perception-Aware Humanoid Design

Problem Statement

Classical robot workspace analysis focuses on kinematic reachability—determining where an end-effector can physically place itself. However, for perception-driven humanoid robots, reachability alone is an incomplete metric. A target may lie within the arm's kinematic workspace but remain outside the field of view of onboard sensors in the specific configuration required to reach it. This "blind-reachable" space forces the robot to perform compensatory whole-body motions (e.g., rotating the torso, walking to a new viewpoint, or redirecting a camera) solely to acquire a view, turning a perception limitation into unnecessary mechanical motion. Existing humanoid designs, often inheriting human form factors with constrained vision concentrated in the head or chest, suffer from a mismatch between broad arm workspaces and limited, often coupled, sensing capabilities.

Methodology

1. Visible-Reachable Workspace (VRW) Definition

The authors introduce the Visible-Reachable Workspace (VRW), a design-stage metric that conditions visibility on feasible reaching configurations.

Configuration Partitioning: The robot's configuration $q$ is partitioned into manipulation joints ( $q_m$ ), sensing joints ( $q_p$ ), and nominal joints ( $q_0$ ). Joints affecting the active end-effector are prioritized in $q_m$ . Crucially, this distinguishes between sensors coupled to the manipulator (e.g., wrist-mounted) and those with independent actuation (e.g., a gimbal).
Conditional Visibility: A target $x$ is considered visible-reachable only if there exists a feasible configuration $(q_m, q_p)$ such that the end-effector reaches $x$ and at least one camera observes $x$ without self-occlusion.
Metrics:
- Coverage ( $\eta$ ): The ratio of the volume of the visible-reachable workspace ( $W_{VR}$ ) to the total reachable workspace ( $W_R$ ).
- Pairwise Coverage ( $\eta_2$ ): A metric for concurrent visibility, measuring the probability that two spatially separated regions (a manipulation target and a second region of interest) can be observed simultaneously without altering the manipulation configuration.

2. Hardware Realization: Duke Humanoid V2

To validate the VRW metric, the authors built Duke Humanoid V2, a 31-DoF quasi-direct-drive (QDD) humanoid.

Morphology: 1.2m tall, 36kg, with two 7-DoF arms and two 6-DoF legs.
Sensing Architecture: The key innovation is the dual independently actuated yaw-pitch camera head. Two RGB-D cameras are mounted on 2-DoF gimbals, allowing them to aim at spatially separated regions independently of the torso heading and arm configuration.
Control: The robot utilizes a whole-body Reinforcement Learning (RL) policy trained with FlashSAC (Soft Actor-Critic), running at 50Hz with 200Hz joint-level PD tracking. The policy handles base locomotion, arm manipulation, and camera gaze simultaneously.

3. Experimental Evaluation

The study evaluates VRW across multiple dimensions:

Cross-Platform Comparison: VRW was calculated for existing humanoids (Unitree G1, Booster T1, Apptronik Apollo, Fourier GR-3, PAL Talos) using their published kinematics and camera models.
Camera Configuration Optimization: On Duke Humanoid V2, the authors compared layouts with $K=1, 2, 3$ cameras, each in either fixed or actuated configurations.
Benchmark Tasks: A "Two-Target Reach-and-Grasp" benchmark was conducted in simulation and on the physical robot. Tasks involved grasping two objects placed in various configurations (left/right, front/back, close/far, and dynamic human-held targets).

Key Results

1. VRW Coverage Improvements

Actuation vs. Count: Camera articulation had a significantly larger impact on VRW coverage than adding more cameras. On Duke Humanoid V2, actuating the cameras increased visible-reachable coverage from 38% (fixed) to 97%.
Pairwise Coverage: While a single actuated camera improved single-target coverage, it could not simultaneously view separated regions effectively. Adding a second independently actuated camera raised pairwise coverage ( $\eta_2$ ) from 0.45 to 0.95. A third camera provided diminishing returns (0.97) for a significant hardware cost.
Comparison: The fixed-head Unitree G1 achieved only 16% VRW coverage. Platforms with actuated necks (e.g., PAL Talos, Fourier GR-3) achieved 48–76%, but all remained below Duke Humanoid V2's 97% because their cameras shared a single neck axis, preventing independent viewing of separated regions.

2. Performance in Manipulation Tasks

In the two-target reach-and-grasp benchmark, the dual-actuated configuration (Act2) outperformed the fixed-camera baseline (Fix2) and other configurations:

Efficiency: Act2 reduced mean completion time by 17% and mechanical energy consumption by 19% compared to Fix2.
Search and Approach: The reduction in time was distributed across search, approach, and manipulation phases. Specifically, camera actuation reduced search time by allowing the robot to locate targets via gaze rather than walking, and reduced approach time by enabling direct paths to targets once located.
Real-World Validation: Physical experiments confirmed that the dual-actuated design allowed simultaneous observation and manipulation of front/back and left/right target pairs without torso reorientation. The robot successfully tracked and grasped moving targets held by two people.

Significance and Claims

The paper claims that reachability becomes a more informative design quantity for perception-driven humanoid manipulation when evaluated together with the sensing configurations that make the reachable space observable.

Design Signal: VRW serves as a quantitative design signal. The results demonstrate that optimizing for visible-reachable coverage (specifically through independent camera actuation) directly translates to more efficient whole-body execution, reducing the need for compensatory body movements.
Coupled Design Principle: The work argues against treating sensing and manipulation as separate modules. Instead, it proposes a coupled design principle where the sensing layout is optimized to maximize the overlap with the manipulation workspace, particularly for concurrent multi-region tasks.
Open Source: The authors commit to open-sourcing the software and the humanoid hardware design (Duke Humanoid V2) to facilitate further research in perception-aware robot design.

The paper concludes that while classical reachability defines where a robot can go, VRW defines where a robot can effectively act while perceiving, and that bridging this gap through actuated sensing is critical for the next generation of humanoid robots.