Environment Design for Reliable Shared Autonomy with Probabilistic Guarantees

Technical Summary: Environment Design for Reliable Shared Autonomy with Probabilistic Guarantees

Problem Statement
Shared autonomy systems aim to assist human operators by inferring intent from noisy inputs and blending human control with autonomous assistance. While prior research has focused on improving intent inference algorithms (e.g., via planning under uncertainty or vision-language models), these approaches typically treat the physical environment as a fixed constraint. This paper identifies a critical gap: the physical arrangement of objects in the workspace fundamentally shapes the difficulty of the inference problem. Specifically, object placement determines the separability of candidate goals under noisy user inputs. Current methods often optimize for "legibility" along a nominal, deterministic trajectory, failing to explicitly model execution noise and its impact on goal distinguishability. Consequently, standard layouts may lead to ambiguous predictions and delayed assistance, particularly in cluttered or high-ambiguity scenarios.

Methodology
The authors propose formulating workspace design as an optimization problem that explicitly accounts for intent inference under noise, deriving a probabilistic correctness guarantee.

1. Probabilistic Inference Model:
   The system utilizes a Boltzmann-rational model to maintain a belief over candidate goals $g$. The probability of a goal is proportional to the efficiency of the observed trajectory $\xi$ relative to that goal. The system commits to a goal when the posterior confidence exceeds a threshold.

2. Margin-Based Correctness Guarantee:
   To ensure robustness against joystick noise, the authors define a pairwise log-posterior margin $M_g(\xi)$ between the true goal $g^*$ and any alternative $g$. Under a bounded Gaussian noise model for user inputs, the terminal state of the robot is modeled as a Gaussian distribution. By linearizing the cost difference around the nominal trajectory, the margin is approximated as a Gaussian random variable.

   The authors derive a sufficient condition for correct goal inference: the system guarantees identifying the true goal with probability at least $1-\alpha$ if the "trajectory margin slack" $s_g(\theta)$ is positive for all competing goals. This slack is defined as the nominal margin minus a term proportional to the margin's variance (sensitivity to noise) and the inverse cumulative distribution function of the failure probability $\alpha$.

3. Optimization Framework:
   The objective is to maximize the worst-case margin slack across all possible true goals and alternatives by optimizing object positions and orientations ($\theta$).

   • Algorithm: Due to the non-convex and multi-modal nature of the layout space, the authors employ MAP-Elites, a Quality-Diversity (QD) optimization algorithm.
   • Behavior Space: To ensure diverse solutions, the archive is indexed by behavioral descriptors: the mean pairwise distance between objects (spatial spread) and the centroid offset from the workspace center (global asymmetry).
   • Constraints: The optimization enforces geometric feasibility, including workspace bounds, inter-object clearance, and collision avoidance with the robot's initial pose.

Key Contributions

• Formulation: The paper formulates workspace design as an optimization problem that explicitly models intent inference under noise, rather than treating the environment as static.
• Theoretical Guarantee: It derives a probabilistic correctness guarantee linking workspace geometry to goal inference reliability, ensuring the true goal is identified with probability $\ge 1-\alpha$ under bounded noise.
• Empirical Validation: The authors demonstrate through simulation that optimized workspaces significantly improve inference reliability and reduce ambiguity compared to random or baseline arrangements.
• Real-World Integration: A real-world shared autonomy system is demonstrated, integrating the inference framework with task-aware workspace optimization.

Experimental Results
Experiments were conducted in simulation across six tabletop scenarios ranging from 2 to 8 candidate goals ($M=2$ to $M=8$).

• Accuracy: Optimized layouts consistently achieved higher argmax accuracy than random baselines. While random layouts degraded significantly as the number of goals increased (dropping to 25% accuracy in the hardest cluttered scenario with $M=8$), optimized layouts maintained near-perfect performance (up to 100% in most cases, 54% in the hardest scenario).
• Inference Speed: In moderate-difficulty scenarios, optimized layouts reduced the time to inference by enabling earlier disambiguation. In high-ambiguity regimes, the primary benefit shifted from speed to robustness, where optimized layouts preserved reliable disambiguation despite increased complexity.
• Optimization Cost: The MAP-Elites optimization process took between 340 and 920 seconds per scene, maintaining high archive coverage (93–100%), indicating the approach scales favorably.
• Real-World Demonstration: The system was tested in three scenarios: making tea with snacks, sorting LEGO blocks, and assistive feeding. In these tasks, the optimized layouts (which separated similar objects) allowed the robot to infer intent earlier and transition to autonomous assistance more effectively than intuitive, clustered baseline arrangements.

Significance and Claims
The paper claims that environment design serves as a "complementary axis" for improving shared autonomy systems. By explicitly shaping the geometry of the inference problem, it is possible to achieve more reliable, predictable, and user-aligned robot behavior without modifying the underlying inference algorithms. The work highlights that physical workspace design is not merely a constraint but a controllable variable that can be optimized to mitigate the effects of human input uncertainty. The authors note that while the current work establishes the theoretical and simulation foundations, future work will involve user studies to evaluate the impact of these optimized workspaces on usability, trust, and task efficiency.