Task-Space Singularity Avoidance for Control Affine Systems Using Control Barrier Functions

2026-03-24

AI Summary

This work proposes a safety-critical control approach based on Control Barrier Functions (CBFs) to address singularity issues in task-space control of affine systems, which arise when the input–output mapping matrix becomes rank-deficient. By continuously monitoring the smallest eigenvalue of this matrix, the method enforces state-dependent safety constraints that proactively steer the system away from singular configurations, thereby preventing trajectory tracking failure and unbounded control effort. To the best of our knowledge, this is the first application of CBFs to task-space singularity avoidance, offering rigorous theoretical safety guarantees that incorporate actuator dynamics while ensuring smooth and bounded control inputs. Simulations on a planar two-link manipulator and a magnetically driven steerable needle demonstrate successful singularity avoidance, stable tracking performance, and up to two orders of magnitude reduction in peak control magnitude.

Technology Category

• Intelligent Robots: Behavior Learning & Control
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Authentication, authorization, and access control
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

Singularities in robotic and dynamical systems arise when the mapping from control inputs to task-space motion loses rank, leading to an inability to determine inputs. This limits the system's ability to generate forces and torques in desired directions and prevents accurate trajectory tracking. This paper presents a control barrier function (CBF) framework for avoiding such singularities in control-affine systems. Singular configurations are identified through the eigenvalues of a state-dependent input-output mapping matrix, and barrier functions are constructed to maintain a safety margin from rank-deficient regions. Conditions for theoretical guarantees on safety are provided as a function of actuator dynamics. Simulations on a planar 2-link manipulator and a magnetically actuated needle demonstrate smooth trajectory tracking while avoiding singular configurations and reducing control input spikes by up to 100x compared to the nominal controller.

Problem

• Task-Space Singularity
• Control Affine Systems
• Singularity Avoidance
• Trajectory Tracking
• Rank Deficiency

Innovation

• Control Barrier Functions
• Singularity Avoidance
• Control-Affine Systems
• Task-Space Control
• Eigenvalue-Based Safety