Formation Control Of Multiple Autonomous Mobile Robots And Stability Analysis

Multiple autonomous robot systems (MARS) have attracted many researchers from the control and robot community in recent years. Many ideas in MARS are inspired by collective animal behaviors observed in nature. In a MARS, like an individual animal, each robot is programmed to sense its local environment, communicate with its neighboring robots, and decide its next movement based on its available information, yet the whole group together can perform desired global tasks. The coordination of multi-robots can improve the performance and complete tasks which are too difficult for a single robot to perform alone. Due to this advantage, there exist numerous potential engineering applications in military surveillance, rescue missions, space and ocean explorations, intelligent transportation systems, and other automated collaborative operations. Among all the coordinated and cooperative control problems, formation control of multiple mobile robots, especially nonholonomic mobile robots is a key problem which is of both theoretical and practical significance.In the first part of this thesis, we explore the distributed formation control of nonholonomic mobile robots. A new cyclic pursuit control law is proposed, where each robot's linear speed and angular speed are proportional to the projection of its prey's position on its forward direction and lateral direction, respectively. Through these interaction a cooperative behavior emerges and the robots eventually move at a constant speed on a circle with constant inter-robot spacings. The control scheme ensures ultimate boundedness and leads to only two stable equilibrium polygons formations. This contrasts with other cyclic pursuit control schemes, where the robots may diverge to infinity and there are more stable equilibrium polygons as the total number of robots increases. For this control scheme, ultimate boundedness is proved using the pseudo-linearization technique. Possible equilibrium polygons are analyzed and stability and convergence properties are established through root locus analysis of a complex characteristic polynomial.In the second part of this thesis, a distributed feedback control strategy that drives a system of multiple nonholonomic robots to a rendezvous point in term of position is introduced. In this control scheme, each robot's linear speed and angular speed are proportional to the sum of the projection of its neighbor robots' positions on its forward direction and lateral direction, respectively. For this control scheme, convergence is proved with the aid of tools from graph theory. Comparing with other discontinuous or(and) time-varying control schemes, ours is easier to be realized from the engineering perspective. Moreover, we prove that our control scheme also works even though actuations might exist for the control inputs. At the end of this part, ultimate boundedness of the system under dynamic sensing graph is proved by pseudo-linearization technique.The third part of this thesis investigates the leader-following formation control of multiple nonholonomic robots. A projection-based control law is proposed and the behavior of the following robot is analyzed. In addition, we use an integral control law to compensate the deformation caused by the acceleration and deceleration of the leading robot and prove that this control scheme can achieve the predesigned formation under certain assumptions.