Nonholonomic Control Utilizing Kinematic Constraints of Differential and Ackermann Steering Based Platforms

A nonholonomic tracking controller is designed and adapted to work with both differential steering and Ackermann steering based platforms whose dynamics are represented using a unicycle model. The goal of this work is to find a relatively simple approach that offers a practical alternative to bulky and expensive algorithms, but still bolsters applicability where many other lightweight algorithms are too lax. The hope is that this alternative will offer a straightforward approach for groups interested in autonomous vehicle research but who do not have the resources or personnel to implement more complex solutions. In the first phase of this work, saturation constraints based on differential drive kinematics are added to ensure that the vehicle behaves intuitively and does not exceed user defined limitations. A new strategy for mapping commands back into a viable envelope is introduced, and the restrictions are accounted for using Lyapunov stability criteria. This stage of work is validated through simulation and experimentation. Following the development of differential drive methods, similar techniques are applied to Ackermann steering kinematic constraints. An additional saturation algorithm is presented, which likewise is accounted for using Lyapunov stability criteria. As with the differential case, the Ackermann design is validated through simulation and experimentation. Overall, the results presented in this work demonstrate that the developed algorithms show significant promise and offer a lightweight, practical solution to the problem of vehicle tracking control.