Abstract
This paper investigates a framework of real-time formation of autonomous vehicles by using potential field and variational integrator. Real-time formation requires vehicles to have coordinated motion and efficient computation. Interactions described by potential field can meet the former requirement which results in a nonlinear system. Stability analysis of such nonlinear system is difficult. Our methodology of stability analysis is discussed in error dynamic system. Transformation of coordinates from inertial frame to body frame can help the stability analysis focus on the structure instead of particular coordinates. Then, the Jacobian of reduced system can be calculated. It can be proved that the formation is stable at the equilibrium point of error dynamic system with the effect of damping force. For consideration of calculation, variational integrator is introduced. It is equivalent to solving algebraic equations. Forced Euler-Lagrange equation in discrete expression is used to construct a forced variational integrator for vehicles in potential field and obstacle environment. By applying forced variational integrator on computation of vehicles' motion, real-time formation of vehicles in obstacle environment can be implemented. Algorithm based on forced variational integrator is designed for a leader-follower formation.
Highlights
Formation of autonomous vehicles has been a hot topic with applications such as formation of UAVs, UUVs, and space satellites [1]
With the methodology introduced for stability analysis, the equilibrium point is proved stable for the error dynamic system
Real-time formation is investigated by using potential field and variational integrator
Summary
Formation of autonomous vehicles has been a hot topic with applications such as formation of UAVs (unmanned aerial vehicles), UUVs (unmanned under-water vehicles), and space satellites [1]. Stability analysis of such nonlinear system is difficult because the stability is mainly about the group structure rather than coordinates of positions Integration of such system plays an important role in real-time formation. Formation of three vehicles and formation based on triangular structures are considered by giving control laws according to vehicles’ geometric relationships in plane [3, 4, 6]. The works of Junge et al for optimal reconfiguration of flying spacecrafts and Kobilarov for discrete geometric motion control of autonomous vehicles have shown the computational advantages of the variational integrator method [20, 23].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
