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Control Barrier Functions for Safe Free-Flying Robotic Spacecraft Operations in Tumbling Target Capture

Alexander Meinert, Peter Stadler, Niklas Baldauf, Alen Turnwald

arXiv:2609.25905v2cs.ROcs.SYeess.SY

TL;DR

Close-proximity capture of uncooperative tumbling targets requires safety constraints across the spacecraft and robotic manipulator, while existing CBF applications cover only subsets of OOS constraints and degrees of freedom. The paper develops a modular, coupling-aware CBF framework and evaluates it in a multi-phase capture scenario, reporting low runtime and retained constraint satisfaction.

  • Problem

    Close-proximity spacecraft capture is safety-critical, and prior CBF-based OOS work covers only subsets of constraints and degrees of freedom.

    Source: §I · p. 1

  • Method

    The framework uses dedicated translational, attitude, and robotic CBF safety filters, passing upstream safe commands downstream as known inputs to account for subsystem coupling.

    Source: §I · p. 2

  • Results

    1.59 ms geometric-mean total runtime was reported, with constraints retained through phase transitions and simultaneous translational, attitude, and robotic motion.

    Source: C. Monte Carlo Simulation · p. 6, B. Numerical Results · p. 6

  • Takeaways & Limitations

    The modular safety layer is demonstrated for 13-DoF robotic OOS capture under CPO guideline constraints, extending the constraint coverage of existing OOS approaches.

    Source: §VI · p. 7

    Contact forces and formal safety guarantees during detumbling remain future work.

    Source: §VI · p. 7

Abstract

from arXiv · show

This paper presents a modular control barrier function (CBF) framework for safe free-flying robotic spacecraft operations during tumbling target capture. Motivated by latest ESA guidelines for safe close proximity operations, safety zones and requirements are translated into dedicated CBFs. The 13-DoF system is decomposed into translational, attitude, and robotic subsystems, each equipped with a safety filter that minimally modifies nominal control inputs in a lightweight quadratic program. The filters enforce a conical approach corridor, collision avoidance zone, attitude line-of-sight pointing, angular velocity limits, robotic joint limits, link-base collision avoidance, and actuator constraints. Dynamic coupling between subsystems is handled by treating upstream safe control commands as known interconnection inputs in the downstream safety filters, preserving modularity while supporting system-level safety. The framework is validated in an on-orbit servicing scenario, including final approach, angular rate synchronization, and tumbling target grasping, using the high-fidelity astrodynamics simulator Basilisk. Monte Carlo simulation results demonstrate runtime efficiency and operational safety for various tumbling rates.

I. INTRODUCTION

The paper develops a modular CBF safety framework for capturing a tumbling target with a free-flying spacecraft, covering 13 degrees of freedom and the relevant OOS mission phases. It translates operational safety requirements into subsystem filters while accounting for dynamic coupling.

I. INTRODUCTION

  • Close-proximity operations are safety-critical, while direct MPC constraint handling can yield non-convex, computationally demanding problems and Hamilton-Jacobi reachability faces a high-dimensionality burden.Source: §I · p. 1
  • Earlier CBF applications to robotic OOS missions covered only subsets of constraints and degrees of freedom, and the cited works did not include tumbling targets.Source: §I · pp. 1–2
  • The framework covers safety constraints across all 13 DoF and the mission phases from final approach through synchronization to robotic grasping.It reflects geometric safety concepts in the latest close-proximity-operation guidelines.Source: §I · p. 2
  • Subsystem safety filters pass upstream safe commands downstream as known interconnection inputs, retaining modularity while accounting for dynamic coupling.The modular structure reflects separate flight-software functions, allows different operating rates and phase-dependent activation, and improves runtime efficiency.Source: §I · p. 2
  • Dedicated CBF constraints address relative translation, attitude pointing and angular velocity, robotic joint limits, link-base collision avoidance, and input constraints.Source: §I · p. 2
  • The approach is validated in a tumbling-target capture scenario using the high-fidelity astrodynamics simulator Basilisk.Source: §I · p. 2

II. CONCEPT OF OPERATIONS

The mission proceeds through final approach, angular-rate synchronization, and capture. The spacecraft model separates translational, attitude, and robotic dynamics, with relative translation expressed in the target-centered Hill frame.

II. CONCEPT OF OPERATIONS

  • The three mission phases are final approach, angular-rate synchronization, and robotic capture, with phases I and II corresponding to the ESA Close Rendezvous phase.During approach, the servicer follows a conical corridor toward the target while entering the spherical Keep-Out Zone; the Collision Avoidance Zone sets a minimum separation to maintain.Source: §II · p. 2

III. PROBLEM STATEMENT

  • The 13-DoF spacecraft has translational, attitude, and robotic subsystems, with spacecraft force and torque inputs and seven manipulator joint torques.Source: §III · p. 2

A. Translational Subsystem

  • Relative translation uses Clohessy-Wiltshire-Hill dynamics for a circular target orbit, with position and velocity represented in the target-centered Hill frame.The actuated translational input is force, and the state and input components correspond to the R-bar, V-bar, and H-bar directions.Source: A. Translational Subsystem · p. 2

B. Attitude Subsystem

C. Robotic Subsystem

The robotic manipulator is modeled relative to the servicer base, with its joint dynamics and end-effector quantities represented through forward kinematics and a geometric Jacobian.

C. Robotic Subsystem

  • The robotic manipulator subsystem is modeled relative to the servicer base frame.Source: C. Robotic Subsystem · p. 3
  • The manipulator model uses a mass matrix, Coriolis and centrifugal forces, and seven-dimensional joint angles, velocities, and accelerations.Source: C. Robotic Subsystem · p. 3
  • Forward kinematics and the geometric Jacobian provide end-effector position and twist, mapped to operational space.Source: C. Robotic Subsystem · p. 3

D. Reference Frame Convention

The reference frame is target-centered and inertially fixed to the servicer’s initial attitude, rather than rotating with the target. The method defines safe sets with CBFs and enforces them through constraints that account for known subsystem coupling.

D. Reference Frame Convention

  • The reference frame FR is target-centered and inertially fixed to the servicer’s initial attitude, so it does not rotate with the tumbling target.Source: D. Reference Frame Convention · p. 3

IV. METHOD

  • A safe set is the zero-superlevel set of a continuously differentiable function h(x, t), and a satisfied CBF condition renders that set forward invariant.Source: §IV · p. 3
  • The method extends position-level safety constraints to relative degree two and enforces them with a CBF condition that includes a discretization offset and maximal control authority.The coupling term ξ is treated as known at each downstream filter, without worst-case maximization or an added disturbance margin.Source: §IV · p. 3

A. CBFs for the Translational Subsystem

The conical approach-corridor CBF accounts for the corridor axis changing in the Hill frame as the reference frame rotates. Its translational safety filter incorporates those time-varying terms while enforcing corridor and input constraints.

1) Conical Approach Corridor Keep-In Zone:

2) Spherical Base Collision Avoidance Zone:

The translational filter encodes the required minimum target distance as a spherical Collision Avoidance Zone and minimally adjusts force commands while maintaining safety and input constraints.

2) Spherical Base Collision Avoidance Zone:

  • The spherical Collision Avoidance Zone enforces a minimum distance between the servicer and target during approach to the Go for Capture decision point.Source: 2) Spherical Base Collision Avoidance… · p. 4
  • The safety constraint uses relative position rH and minimum safety distance RCAZ in the repeatedly solved translational safety-filter QP.Source: 2) Spherical Base Collision Avoidance… · p. 4
  • The filter minimally adjusts nominal force fH,nom to maintain the corridor, Collision Avoidance Zone, and input constraints; affine constraints support runtime-efficient online implementation.The resulting safe force is transformed to the servicer body frame as fB,SF.Source: 2) Spherical Base Collision Avoidance… · p. 4

B. CBFs for the Attitude Subsystem

The attitude subsystem uses a time-varying line-of-sight cone constraint to keep the target within the sensor cone. Its CBF accounts for changing target geometry and servicer motion, with translational input treated as a coupling term.

B. CBFs for the Attitude Subsystem

  • The attitude keep-in zone keeps the target within the admissible sensor cone, addressing collision avoidance and camera-based perception of the grasping point.An end-effector-mounted camera alone is insufficient in close proximity.Source: B. CBFs for the Attitude Subsystem · p. 4

1) Time-Varying Attitude Cone Keep-In Zone:

  • The line-of-sight direction runs from the servicer base to the target grasping point, whose target-fixed location is transformed into the reference frame as the target tumbles.Source: 1) Time-Varying Attitude Cone Keep-In… · p. 4
  • The attitude cone CBF uses the admissible half-cone angle βATT; its time variation reflects both changing line of sight and servicer motion, with translational input entering as ξatt.The attitude torque appears in the second time derivative of the barrier function.Source: 1) Time-Varying Attitude Cone Keep-In… · p. 4

2) Servicer Angular Velocity Limits:

The attitude safety filter enforces component-wise servicer angular-velocity limits alongside attitude-cone and input constraints. The robotic subsystem separately constrains each joint angle, accounting for upstream safe force and attitude commands.

2) Servicer Angular Velocity Limits:

  • Servicer angular velocity is bounded component-wise in the body frame, with torque constraints enforced through relative-degree-one CBF conditions.The attitude safety-filter QP minimizes deviation from nominal torque while satisfying attitude-cone, angular-velocity, and input constraints.Source: 2) Servicer Angular Velocity Limits · pp. 4–5

1) Robotic Joint Angle Limits:

  • Each manipulator joint angle is constrained to its admissible range using a CBF that accounts for upstream safe force and attitude commands.Joint torque enters the second derivative of the angle constraint.Source: 1) Robotic Joint Angle Limits · p. 5

2) Robotic Joint Velocity Limits:

The robotic safety filter constrains joint velocities and prevents manipulator links from colliding with the servicer base. Its link-base CBF uses collision spheres, a conservative geometric approximation.

2) Robotic Joint Velocity Limits:

  • Joint-velocity bounds are enforced with relative-degree-one CBF conditions because joint torque enters the velocity derivative through the robotic dynamics.The joint-velocity limits are component-wise.Source: 2) Robotic Joint Velocity Limits · p. 5

3) Spherical Link-Base Collision Avoidance:

  • Link-base collision avoidance models each robotic link with collision spheres and keeps each sphere outside the spherical base collision zone.The sphere-based model is conservative; capsules or ellipsoids may reduce conservativeness for some geometries but can increase computational cost.Source: 3) Spherical Link-Base Collision… · p. 5

V. ON-ORBIT SERVICING SIMULATION STUDY

The study pairs unconstrained nominal controllers with a CBF safety layer to demonstrate how filtering addresses their unsafe commands. Figure 4 summarizes safety-filter satisfaction and nominal-controller violations across the translational, attitude, and robotic subsystems.

A. Nominal Controllers

  • The nominal controllers use MPC for translation and attitude and a joint-space PD computed-torque controller for the manipulator.The MPC constraints are inactive to produce unsafe nominal inputs and demonstrate constraint satisfaction by the safety layer.Source: A. Nominal Controllers · pp. 5–6
  • Figure 4 compares safety-filter constraint satisfaction with nominal-controller violations across the translational, attitude, and robotic subsystems.It also shows range-rate, synchronization-error, and grasping joint-torque profiles.Source: Figure 4 · p. 6

B. Numerical Results

The simulations show that the modular safety filters maintain operational constraints through mission phases and simultaneous subsystem motion. Across 100 Monte Carlo trajectories, the filters remain operationally safe with millisecond-scale runtime, while higher tumbling rates are associated with greater robotic effort and modestly larger synchronization error.

B. Numerical Results

  • The modular safety layer retained constraint satisfaction through phase transitions and simultaneous translation, attitude synchronization, and robotic motion.Robotic intervention was driven primarily by joint-velocity and torque constraints rather than self-collision avoidance.Source: B. Numerical Results · p. 6

C. Monte Carlo Simulation

  • 1.59 ms was the geometric-mean total runtime, with a 3.75 ms maximum against a 100 ms controller sample time.All subsystem QP runtimes remained below 2.3 ms; the attitude filter required the most computation.Source: C. Monte Carlo Simulation · p. 6, Figure 5 · p. 6
  • Across 100 trajectories, every closed-loop approach and attitude trajectory satisfied the operational zones, while higher tumbling rates were associated with greater robotic effort and moderately larger synchronization error.The peak grasping synchronization error was approximately 0.0432-0.0457 rad/s, below errors of up to 0.3 rad/s during the preceding synchronization phase.Source: C. Monte Carlo Simulation · pp. 6–7, Figure 6 · p. 7

VI. CONCLUSION

  • Contact forces and formal safety guarantees during detumbling remain future work.The framework incorporates extensive CBF constraints for a 13-DoF spacecraft in line with close-proximity-operation guidelines.Source: §VI · p. 7

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