Dual Path Following for an Aerial Manipulator Under State and Input Constraints via Transverse Feedback Linearization

Hamza Tariq; Adeel Akhtar

cs.RONov 1, 2026

Dual Path Following for an Aerial Manipulator Under State and Input Constraints via Transverse Feedback Linearization

Authors: Hamza Tariq, Adeel Akhtar

Organizations: Department of Mechanical & Industrial Engineering at the New Jersey Institute of Technology, Newark, NJ 07102, USA.

Abstract

This paper studies dual path following for a quadrotor carrying a three-degree-of-freedom arm. The center of mass of the combined system must follow a vehicle path and the end effector must follow a second path, while the arm respects its joint limits and avoids its singular postures. The vehicle and the arm are mechanically coupled, so one controller must handle both paths. With the center of mass and the end-effector path coordinates as outputs, and a dynamic extension of the thrust, the system admits a normal form without internal dynamics. We characterize the states where this normal form fails. We formulate the transverse feedback linearizing controller as a quadratic program that relaxes only the speed of the end effector along its path and imposes safety and actuator limits as inequality constraints. The program reduces to a scalar problem with a closed-form solution. If it remains strictly feasible for all time, the feedback is locally Lipschitz, both paths are invariant and attractive, and every constraint holds. In the physics engine Drake, the controller resolves a conflict between the two speed references by slowing the end effector while both paths remain invariant. By contrast, a cascade with a safety filter leaves both paths. Code and animations are available at https://gradslab.github.io/am_dual_pf-/

Figures & tables

Fig. 1: Dual path following in Drake. The center of mass $p_{c}$ of the combined system follows the vehicle path $\gamma_{c}$ (blue, dotted) and the end effector $p_{e}$ follows the end-effector path $\gamma_{e}$ (red, dotted). The solid red line is the recent end-effector trajectory.

Fig. 2: Nominal controller from an off-path start (dots). Left: center of mass (blue), end effector (red) and paths (wide light lines). Right: distances to the paths, along-path speeds and heading error.

Fig. 3: Incompatible speed references: distances to the paths, along-path speeds with references (gray dotted),

\vartheta_{2}

and

\det J_{\rho}

with limits and margin (black dash-dotted). The gray line marks the switch at

t=15

s. The nominal run diverges at the cross, and the cascade speeds leave the plotted range.

Feedback Control

Feedback control uses ongoing measurements to adjust actions, stabilize dynamical systems, track goals, and respond to disturbances and constraints.

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Decentralized Safe Path Following for Multiple Quadrotors on Intersecting Paths with Theoretical Guarantees

Hamza Tariq, Adeel Akhtar

Department of Mechanical & Industrial Engineering at the New Jersey Institute of Technology, Newark, NJ 07102, USA

Quadrotor Control Multi-Robot Coordination Robot Collision Avoidance Robot Trajectory Tracking

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This paper studies decentralized safe path following for multiple quadrotors on intersecting paths, where safety requires both collision avoidance and strict adherence to pre-assigned routes. The proposed controller reformulates transverse feedback linearization as a constrained quadratic program with four equality constraints: two enforce convergence to and strict adherence to the path, and two prescribe the desired speed and heading. Safety is achieved by relaxing only the along-path speed constraint, while the path and heading constraints remain hard. Under the stated assumptions, and for admissible initial conditions, the controller guarantees that all agents converge to and thereafter follow their assigned paths, avoid collisions, and avoid attitude singularities. We evaluate the controller in the Drake physics engine on non-planar intersecting paths and compare it against two nominal-plus-safety-filter cascades. Code and additional results are available at https://gradslab.github.io/safe_multiquad_pf/.

Abstract

Feedback Control

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