Feedback Linearization has been used extensively in robotics as a means of controlling complicated nonlinear systems. However, exact computation can prove to be expensive in terms of hardware/software requirements for real time control. In the design of the feedback linearized control system for the hexapod, we show that it is sufficient to perform nonlinear cancellation of the most significant terms arising from the local dynamics at each leg, without compromising on the overall performance of the system. The performance of different controllers and gait algorithms can then be investigated using the animation package developed for this purpose.
The kinematics of the hexapod was modeled and approximated using a Fourier Series Expansion in terms of the various dynamical parameters. Using a Lagrangian approach, we formulated the dynamics of the hexapod on the assumption that it was walking on level ground without slipping. A study was then performed on the nonlinear dynamics of the system to determine the minimum number of terms required to perform decentralised feedback linearisation. Once this was achieved, a nonlinear dynamical model employing the suggested control architecture was constructed on SIMULINK. This model also incorporated the effect of static/viscous friction from the gears, the effect of current/voltage saturation of the various analog devices e.g. amplifiers and the torque/speed limitations of the motors used. In addition some gait algorithms were also devised for walking on level ground.
The decentralised control system performs well in tracking the various gait algorithms. The steady state error of the system is small and can be reduced with improved tuning of the PID controllers employed. Another advantage with decentralised control is that the control algorithm can easily be modified in the event that weight of the different components of the hexapod changes.
In this project we have shown that it is possible to implement advanced nonlinear control laws in a fairly inexpensive manner and achieve good performance with the added flexibility of modifying the control algorithms with ease.
We hope to perform real time animation of the hexapod in order to provide a comprehensive design and testing methodology prior to actual fabrication and testing. Furthermore, it is hoped that we can direct our work to control and gait algorithms on non-smooth terrain.