Robust control strategies in task space for uncertain dynamical systems with input saturation

In the realm of engineering, dynamical systems are frequently tasked in the context of task space, which aligns more closely with the intuitive approach engineers take when devising controllers to adhere to task space constraints rather than those in joint space. This article introduces control methodologies in the task space for dynamical systems subject to input saturation constraints. The dynamical systems are characterized by an uncertainty that changes over time, which could be rapid, and is confined within limits that are not known. Two distinct types of control schemes, both initiated from the Udwadia-Kalaba (U-K) equation, have been put forward with the aim of ensuring the convergence of tracking errors. The first controller does not take into account the limitations of input saturation and is structured into three distinct parts: a nominal controller formulated from the U-K equation, a feedback controller that responds to errors in task space tracking, and a compensatory controller that forecasts the bounds of uncertainty. The controller’s design is facilitated by a Lyapunov approach, which also serves to ensure its stability. The second controller takes into account the issue of input saturation, proposing a controller in a switching form, which has been rigorously validated through the application of Lyapunov’s stability theory. The introduction of these two controllers expands the scope of the Udwadia-Kalaba equation’s application to task space control within uncertain dynamical systems. To elucidate and exemplify our control strategies, simulations are conducted using a 2R manipulator.