Adaptation Mechanism of Asymmetrical Potential Field Improving Precision of Position Tracking in the Case of Nonholonomic UAVs

Abstract

SummaryPosition-tracking problems in the structures of rigid formations of nonholonomic mobile robots, such as fixed-wing unmanned aerial vehicle (UAVs), must reconcile tracking precision and flight stability, which usually exclude each other due to nonholonomic motion constraints. Therefore, a position-tracking control that is based on distance and position displacement, defined as inputs of control loops, requires the application of dead zones around target positions, which are the points of instability. For this reason, the control becomes sensitive to any external disturbance causing oscillations of control signals and so it becomes difficult to maintain a zero value of position displacement over a long time horizon. Thus, we propose an approach based on the adaptive mechanism of an asymmetrical local artificial potential field, which is defined by a local frame of reference whose origin is located in the tracked position of a UAV in the formation frame. It couples controls of both airspeed and heading angle into a nonlinear potential function of relative position and orientation with respect to the tracked position and adapts it according to heading rate of the leader. The function splits the area around the tracked position longitudinally into two zones of acceleration and deceleration; therefore, velocity vectors are longer (higher airspeed) only when a UAV is behind the tracked position and shorter (lower airspeed) when it is ahead. The area is laterally symmetrical, and orientations of velocity vectors align asymptotically to the longitudinal direction accordingly with the decrease in the lateral error. Finally, velocity vectors are rotated proportionally to the heading rate of the leader, which improves the tracking precision during turns. If we assumed that a UAV’s tracked position is in motion, it could easily be proven that the position control based on the adaptive asymmetrical potential function becomes asymptotically stable in the tracked position. Numerical simulation verifies this thesis and presents more precise and stable position tracking due to the adaptation mechanism.

Self-Adaptive Asymmetrical Artificial Potential Field Approach Dedicated to the Problem of Position Tracking by Nonholonomic UAVs in Windy Enivroments

“…The second section presents new definitions of potential function gradient and VVF, which are based on the asymmetrical potential function approach modified by a self-adaptive mechanism applying integrals of tracking error. In the third section, the results of numerical simulations compare responses to a step change of wind velocity in the cases of the proposed novel self-adaptive asymmetrical potential function approach and the previous approach from Kownacki and Ambroziak (2019). The conclusions and discussion are in the final section.…”

“…In numerical simulations, the same dynamical model of a fixed-wing UAV was utilised as in works of Kownacki and Ambroziak (2017) and Kownacki and Ambroziak (2019). The UAV's dynamics are defined by a set of six differential equations, namely Eqs ( 9) and ( 10):…”

“…The definition of the asymmetrical potential function is used to create a velocity vector field (VVF), which guides a fixed-wing UAV in a way that smoothly aligns its heading and airspeed to the heading angle and airspeed of the tracked point. In the subsequent work (Kownacki and Ambroziak, 2019), the approach is modified by expanding it by a rotation mechanism of the VVF. It counteracts increments of tracking error during manoeuvres as the result of formation rotation when a UAV is behind the leader and the tracked position.…”

“…The slope of the potential function, spatial orientation and lengths of gradients and velocity vectors will be changing depending on wind drift incrementing the integrals' values. Therefore, the main contribution of this work is defining a new approach to the asymmetrical potential function from works of Kownacki and Ambroziak (2017) and Kownacki and Ambroziak (2019), which considers integrals of position tracking errors so as to minimise them in the case of wind drift effect.…”

Efficient Non-Odometry Method for Environment Mapping and Localisation of Mobile Robots

“…In recent years, robotics researchers have shown an increasing interest in autonomy of mobile vehicles. The autonomy of robots is mainly associated with obstacle detection and avoidance systems (Gao et al, 2019;Rulin, 2017), precise navigation systems (Romaniuk et al, 2016;Bakkali et al, 2007), new control methods allowing adaptation to failures (Ambroziak et al, 2019;Lanzon et al, 2014), cooperation of a few objects, and formation and swarm motion (Ambroziak et al, 2015;Kownacki et al, 2019). Mentioned topics relate to tasks carried out by mobile robots in indoor and outdoor conditions.…”