The continuous dynamic model of a robot is represented by nonlinear coupled differential equations. These can be discretized using first or second order Taylor's series approximations. One such model, the Greenspan Discrete Mechanics model appears to be the best for control applications. Global linearization of this model is straightforward and the linearized model is used to design l\sp1 optimal controllers for the robot. The Multi Input Multi Output optimization problem splits up into decoupled Single Input Single Output problems which are individually solved. Optimal systems thus designed are simulated and compared to traditional robot controllers. Simulations confirm the l\sp1 optimality of the controllers. This thesis thus provides a useful new tool for the robot control engineer.