Safe Robotics: Guiding Robots Through Tight Spaces

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Author: Denis Avetisyan

A new approach leverages geometric shapes and distance fields to enhance collision avoidance and improve robot maneuverability in complex environments.

This paper presents a novel safety filtering framework using superquadrics and signed distance functions for robust and numerically stable robot control.

Ensuring robotic safety in complex environments remains challenging due to limitations in geometric representations used for collision avoidance. This paper, ‘SQ-CBF: Signed Distance Functions for Numerically Stable Superquadric-Based Safety Filtering’, addresses this by introducing a novel safety filtering framework leveraging superquadrics and signed distance functions. We demonstrate that formulating safety barriers using signed distance functions-computed efficiently via the Gilbert-Johnson-Keerthi algorithm and smoothed for gradient stability-overcomes ill-conditioning issues inherent in direct use of implicit superquadric functions. Does this approach pave the way for more robust and efficient real-world robotic manipulation in increasingly cluttered and dynamic scenes?

The Illusion of Predictability

Conventional robotic control systems, designed primarily within the predictable confines of laboratory settings, frequently encounter difficulties when deployed in unstructured, real-world environments. These systems often rely on precise models of the robot and its surroundings, an assumption quickly invalidated by the inherent uncertainties of dynamic spaces – unexpected obstacles, slippery surfaces, or variations in object properties. Consequently, even minor discrepancies between the programmed plan and the actual environment can lead to collisions, damage, or even safety hazards. The challenge isn’t a lack of power or dexterity, but rather the inability of these traditional methods to reliably adapt to the unpredictable nature of real-world interaction, necessitating the development of more robust and adaptive control strategies.

Effective robotic manipulation in unpredictable environments hinges on the implementation of robust safety filters capable of preventing collisions. These filters function as a crucial layer of defense, constantly monitoring planned trajectories and intervening to adjust movements before contact occurs with obstacles or humans. However, designing such filters presents a significant computational challenge, particularly as task complexity increases – more intricate motions demand faster processing to maintain real-time responsiveness. The ideal safety filter must strike a delicate balance: it needs to be highly sensitive to potential hazards to ensure safety, yet computationally efficient enough to avoid hindering performance or introducing noticeable delays in execution, enabling robots to navigate dynamic workspaces with both precision and security.

Existing safety mechanisms for robotic manipulation often present a frustrating trade-off between caution and usability. Many systems prioritize preventing any potential collision, resulting in overly conservative behavior that hinders a robot’s ability to perform delicate or nuanced tasks. This excessive caution can manifest as slow movements, abrupt stops, or a refusal to attempt maneuvers that, while carrying a small risk, would be easily executed by a human operator. Conversely, some approaches prioritize speed and responsiveness, potentially sacrificing safety margins and increasing the likelihood of unintended contact. This lack of responsiveness makes intuitive teleoperation-where a human operator guides the robot in real-time-extremely difficult, as the system may not react quickly enough to correct errors or adapt to unforeseen circumstances, ultimately limiting the robot’s practical application in dynamic and unpredictable environments.

Mapping the Chaos: Superquadrics and Safety

The SQ-CBF framework represents both the robot and its surrounding environment using superquadrics – a class of mathematical surfaces defined by the equation |x|^p + |y|^p + |z|^p \le 1, where ‘p’ controls the shape and can be adjusted to approximate a variety of geometries. This approach offers a computationally efficient method for representing complex shapes with a limited number of parameters, enabling real-time collision detection and safety verification. Superquadrics are particularly advantageous due to their analytical differentiability, which is essential for gradient-based optimization algorithms used within the Control Barrier Function (CBF) formulation. By representing all entities as superquadrics, the system simplifies geometric reasoning and facilitates the calculation of distances needed to enforce safety constraints during motion planning.

Signed distance functions (SDFs) represent the shortest distance from any point in space to a surface. The SDF value is positive when the point is outside the object, negative when inside, and zero on the surface itself. Crucially, SDFs are continuously differentiable, even at surface intersections, enabling the use of gradient-based optimization techniques. This differentiability is essential for formulating control laws where safety constraints are expressed as inequalities, allowing for smooth and reliable adjustments to robot trajectories during planning and execution. The value and gradient of the SDF provide both magnitude and direction of the closest approach, facilitating the calculation of safe velocities and ensuring collision avoidance in dynamic environments. SDF(x) = \min_y ||x - y|| , where y is a point on the surface.

Control Barrier Functions (CBFs) are extended within the SQ-CBF framework to provide explicit safety guarantees during robot motion planning. Traditional CBFs define a safety margin around the robot, ensuring that a safety function remains positive during trajectory execution, indicating a safe state. The SQ-CBF approach integrates these functions directly into the optimization process used for trajectory generation. By formulating safety constraints as part of the optimization problem, the planner actively seeks trajectories that not only achieve the desired goal but also demonstrably satisfy the defined safety criteria. This is achieved by penalizing any trajectory that would violate the CBF constraints, effectively guiding the planner towards safe and feasible motions. The resulting trajectories are therefore guaranteed to maintain a specified safe distance from obstacles and adhere to the defined operational limits.

The Algorithm’s Embrace: Efficiency Through Computation

The Gilbert-Johnson-Keerthi (GJK) algorithm is utilized to efficiently determine the distance between superquadric surfaces, forming the basis for Signed Distance Field (SDF) calculation. GJK operates by iteratively refining a supporting simplex until the minimum distance between the convex hulls of two shapes is found. This distance represents the shortest path between the surfaces and is a critical component in defining the SDF value at any given point in space. By leveraging GJK’s ability to efficiently compute distances between convex shapes, the computational cost associated with SDF generation is significantly reduced, enabling real-time performance in applications like collision detection and path planning. The algorithm avoids explicit representation of surfaces, operating directly on supporting features to improve performance.

Implicit superquadric functions, while capable of representing complex shapes, exhibit ill-conditioning which negatively impacts gradient estimation for Signed Distance Field (SDF) computation. To mitigate this, we employ randomized smoothing. This technique involves perturbing the superquadric surface with a small, random displacement during gradient calculation. By averaging gradients computed across multiple random perturbations, the effects of ill-conditioning are reduced, yielding more stable and reliable SDF gradient estimates. The magnitude of the random displacement is carefully tuned to balance smoothing effectiveness with preservation of geometric detail, ensuring accurate SDF representation without excessive blurring.

The Minkowski Difference, denoted as A ⊖ B, is a set operation used in Signed Distance Field (SDF) computation to determine the distance between two objects, A and B. Specifically, it represents the set of all points x such that x + B is contained within A. In the context of SDFs, computing the Minkowski Difference allows for the efficient calculation of the distance from a point on the surface of object A to the closest point on the surface of object B. This distance is then used to define the SDF value at that point, with the sign indicating whether the point is inside or outside of object B. Utilizing the Minkowski Difference facilitates a robust and geometrically accurate method for determining the distance between complex shapes, which is crucial for collision avoidance and other geometric reasoning tasks.

Quadratic Programming (QP)-based optimization is implemented to resolve Control Barrier Function (CBF) constraints and calculate safe control inputs for the system. This approach enables real-time performance, consistently achieving cycle times of ≤ 10 ms, even when managing up to 800 potential collision pairs. The QP formulation transforms the CBF constraints into a quadratic cost function subject to linear inequality constraints, allowing for efficient solution via established optimization solvers. Furthermore, the implementation leverages multi-core processing to parallelize the computation, significantly reducing the time required to solve the QP problem and maintain responsiveness in dynamic environments.

The System’s Reach: Validation and Teleoperation

Rigorous testing of the developed framework utilized a Franka Emika FR3 robot, pushing its capabilities within realistically complex environments. The system consistently demonstrated a 100% success rate in avoiding collisions, a crucial benchmark validated through both detailed simulations and demanding real-world experiments. This achievement highlights the robustness and reliability of the approach, confirming its potential for deployment in scenarios requiring safe and dependable robotic navigation. The consistent performance across both virtual and physical testing underscores the framework’s ability to translate effectively from controlled environments to unpredictable, real-world applications, paving the way for increased autonomy and human-robot collaboration.

The research successfully merged a Safety Quadratic Control Barrier Function (SQ-CBF) filter with a teleoperation interface, resulting in a system that allows for intuitive and, crucially, safe remote control of a robotic arm. This integration addresses a key challenge in teleoperation – maintaining safety when a human operator isn’t directly perceiving the robot’s surroundings. The SQ-CBF filter acts as a protective layer, continuously monitoring for potential collisions and modulating the robot’s movements to prevent them, even if the operator’s commands would otherwise lead to an unsafe action. This allows operators to control the robot with a natural feel, confident that the system will autonomously enforce safety constraints and prevent damage to the environment or the robot itself.

A robust and unified control architecture is central to the system’s functionality, achieved through the implementation of the CRISP framework – a modular design enabling seamless integration of low-level control and state feedback mechanisms. This framework facilitates precise robot actuation and responsive adjustments based on real-time environmental perception. By consolidating these core control elements, CRISP allows for a streamlined and efficient flow of information, improving the robot’s ability to react to dynamic changes and execute tasks with greater stability and accuracy. The modularity also promotes scalability, simplifying future enhancements and adaptations to different robotic platforms or complex manipulation scenarios.

Accurate perception of the environment is crucial for successful robotic manipulation, and this system achieves robust obstacle tracking through the integration of the Extended Kalman Filter and Iterative Closest Point algorithms. The Extended Kalman Filter predicts and updates the state of dynamic obstacles, effectively anticipating their movements, while Iterative Closest Point refines this estimation by precisely aligning sensor data with the perceived environment. This combined approach enables the robot to not only detect but also predict the trajectories of moving objects, leading to a significant 39% average improvement in task completion time during simulated teleoperated manipulation scenarios. The system’s ability to anticipate obstacle movement allows for smoother, more efficient robot motion, minimizing unnecessary stops and adjustments and ultimately enhancing the overall performance of remote control tasks.

The pursuit of robust robotic systems necessitates acknowledging their inherent complexity. This work, focused on superquadric-based safety filtering, embodies this understanding. A system isn’t a machine, it’s a garden – and this framework cultivates resilience through nuanced geometric representation. As Tim Berners-Lee once stated, “The Web is more a social creation than a technical one.” Similarly, this approach recognizes that effective collision avoidance isn’t solely about precise calculations, but also about creating a forgiving interplay between robot and environment. The signed distance functions act as that forgiveness, allowing for more adaptable and reliable operation within dynamic, cluttered spaces. It’s a testament to the idea that systems grow, they aren’t simply built.

What’s Next?

The pursuit of numerically stable safety guarantees, as demonstrated by this work, inevitably reveals the fragility inherent in any geometric abstraction. Superquadrics, though elegant, remain a simplification of a world stubbornly resistant to neat mathematical description. The true challenge isn’t crafting a perfect filter-such a thing is a static delusion-but designing systems that gracefully degrade when confronted with the inevitable discrepancies between model and reality. A system that never breaks is, after all, a system that never learns.

Future efforts will likely focus not on ever-more-complex representations, but on methods for actively embracing uncertainty. The current paradigm treats collision avoidance as a boundary to be meticulously maintained. A more resilient approach might explore temporary, controlled breaches of those boundaries-allowing for brief, self-corrected incursions into forbidden space as a means of navigating genuinely unpredictable environments. Perfection, predictably, leaves no room for people – or for the chaotic contingencies of the physical world.

Ultimately, this line of inquiry is less about robotics and more about epistemology. The question isn’t simply whether a robot can avoid a collision, but what it means to know a collision is avoidable. The very notion of “safety” is revealed as a perpetually shifting target, a testament to the limitations of any predictive model. The next iteration will not be a better filter, but a more honest assessment of what a filter can, and cannot, achieve.

Original article: https://arxiv.org/pdf/2602.11049.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2026-02-12 17:43