Steering Three-Input Chained Form Nonholonomic Systems Using Sinusoids: The Fire Truck Example

In this paper, we steer nonholonomic systems with linear velocity constraints repre sented mathematically in a special form, called chained form. We observe that chained form systems can be steered from an initial configuration to a final configuration with sinusoidal inputs. The controller we use is open loop and no special provisions are made for obstacle avoidance. Sufficient conditions are presented for converting a threeinput system with nonholonomic velocity constraintsinto a "two-chain, single-generator chained form." An algorithm is stated that constructs the sinusoidal control inputs to steer this system from any initial configuration to any desired final point. Our example of a three-input nonholonomic system is a firetruck, or tiller truck. In this three-axle system, the control inputs are the steering velocities of both the front and rear wheels of the truck and the driving velocity of the truck. Simulation results are given for the familiar parallel parking problem and other trajectories.