We present a method for real-time computation of clothoid coordinates that guarantees bounded approximation error over a wide range of clothoid parameters provided that the clothoid's orientation change and length are bounded. It is shown that coordinates of clothoid with any parameters can be computed from those of a single clothoid (with fixed parameters), using appropriate geometrical transformations. A comprehensive analysis is given on how to determine a required set of clothoids and, based on this, how to sample a clothoid in a lookup table in order to achieve required approximation precision. The algorithm is computationally very efficient and therefore suitable for real-time path planning, as well as for other applications that benefit from fast clothoid computation.
This paper presents an experimental overview of common trajectory tracking methods for nonholonomic mobile robots: linear control, nonlinear control and model predictive control. All methods are compared experimentally on a two-wheel mobile robot with differential drive. The goal was to determine which control method is the best with respect to robustness and low trajectory tracking error. Thereby, a special emphasis is given on a fast real-time trajectory tracking and behavior in conditions near robot velocity and acceleration limits.
This paper is concerned with the problem of finding an optimal velocity profile along the predefined path in order to traverse the path in shortest time. A dynamic model of the mobile robot that accounts for robot actuator constraints is derived. It is shown how to use this dynamic model to express acceleration limits and velocity limit curve required by the optimal time-scaling algorithm. The developed trajectory planning algorithm is demonstrated on the Pioneer 3DX mobile robot. A method is very flexible and can be extended to account for other constraints, such as limited grip between the robot wheels and the ground.
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