Kinematic motion planners are among the most widely used control approaches in robotic applications. By modeling the robot as a first-order system, they generate a feedback-based desired velocity field that guides the robot toward a target while avoiding obstacles. However, extending such feedback planners to systems with higher-order dynamics, while preserving safety and stability properties, is not a straightforward task. In the present work, we propose an approach that adapts existing feedback-based kinematic motion planners to second-order autonomous systems while retaining their safety and almost global asymptotic stability guarantees. We consider two general classes of kinematic motion planners: those derived from navigation functions and those defined directly through desired velocity fields without relying on an underlying navigation function. To validate the proposed methodology, two feedback-based kinematic motion planners are adapted to second-order systems and evaluated both in simulations and experimentally.
Figures & tables
Fig. 1 : Block diagram illustrating the adaptation of the feedback-based kinematic motion planners to second-order dynamics via obstacle-aware damping.
Fig. 2 : Block diagram of the dynamic damping feedback controller ( 8 ).
Fig. 3 : Block diagram of the velocity tracking feedback controller ( 11 ).
Fig. 4 : Plots obtained using the DDF and VTF control laws with vd defined in ( 19 ). (a)-(c) Plots of dr(x) , ∥v∥ and ∥ud∥ versus time obtained using the DDF control law. (d)-(f) Plots of dr(x) , ∥v∥ and ∥uv∥ versus time obtained using the VTF control law.
Fig. 5 : x -trajectories under the DDF (solid curves) and VTF (dashed curves) control laws with vd defined in ( 19 ).
Fig. 6 : Plots obtained using the DDF control law with vd defined in ( 21 ). (a) Point robot trajectories in the star world. (b) Point robot trajectories in the transformed sphere world. (c)-(e) Plots of dr(x) , ∥v∥ and ∥ud∥ versus time.
Fig. 7 : Plots obtained using the VTF control law with vd defined in ( 24 ). (a)-(d) Plots of dr(x) , ∥v∥ , ∥uv∥ and ∥v−vd(x)∥ versus time.
Fig. 8 : x -trajectories under the VTF control law with vd defined in ( 24 ).
Fig. 9 : Implementation of the proposed control strategies on the Quanser QDrone 2.
Fig. 10 : Quanser QDrone 2 used for experimental validation.
Fig. 11 : QDrone2 trajectory under the DDF control law.
Fig. 12 : QDrone2 trajectory under the VTF control law.
Fig. 13 : Top view of the quadrotor trajectories under the proposed control strategies.
Fig. 14 : Comparison of the proposed control strategies, with magenta curves obtained under the DDF control law and blue curves obtained under the VTF control law. (a) Norm of the horizontal component of the quadrotor velocity versus time. (b) Norm of the horizontal component of the control input vector versus time.