In a leader/follower formation, the lead robot is controlled through a nonholonomic system
, meaning that the trajectory is set in advance, and the followers are tracing the same pattern that the leader takes by using sonar.
This paper presents the application of genetic algorithms in the solution of motion planning problem in mobile robots for a two-dimensional environment without uncertainties and with a model of mobile three-wheeled robot with characteristics than classify it like a nonholonomic system
The kinematic model for a drift-free nonholonomic system is given as
A unicycle model or a two-wheel car model, shown in Figure 1, is basically a three-dimensional nonholonomic system having two inputs and three states with depth-one Lie bracket.
A front wheel car model, shown in Figure 2, is basically a four-dimensional nonholonomic system having two inputs and four states with depth-two Lie bracket.
A car with trailer model, shown in Figure 3, is basically a five-dimensional nonholonomic system having two inputs and five states with depth-one, depth-two, and depth-three Lie brackets.
Mobayen, "Finite-time tracking control of chained-form nonholonomic systems
with external disturbances based on recursive terminal sliding mode method," Nonlinear Dynamics, vol.
In , the underactuated nonholonomic systems with chained form were investigated by output feedback control law; the designed controller rendered the state variables to zero within finite time.
In , a class of nonholonomic systems in chained form which can model mobile robots and wheeled vehicles was studied, the finite time state feedback controller was addressed; however, the method requires the sway velocity satisfying the first-order nonholonomic constraints (the sway velocity must be zero); it cannot be applied to the control of UAVs.
Zhang, "Finite-time stabilization of uncertain nonholonomic systems in feedforward-like form by output feedback," ISA Transactions, vol.
Besides they have proved to be useful in Mechanics [2, 4, 7, 16, 24], in the theory of nonholonomic systems
[3, 9, 18] in control theory , in field theory , in quantum and classical gravity [22, 23].
His research applies to both theory and applications in a wide range of problems, including nonholonomic systems
, space and mobile robots, haptic interfaces and robots for telesurgery and remote diagnostics, control of structural vibration, and control of rotors supported by magnetic bearings.