Advanced Topics in Nonlinear Programming and Its Application in Robotic Control

Dear Colleagues,

Optimization algorithms play a crucial role in any practical, real-world system. Since the goal of an optimization algorithm is to find an optimal solution for a given objective function, this goal becomes extremely difficult in the case of a nonlinear objective function. Unlike linear optimization, where the solution space is typically convex and solutions can be found using straightforward algebraic techniques, nonlinear optimization often presents challenges due to multiple local optima, non-convexities, and complex constraints. However, most real-world systems are nonlinear, making it challenging to accurately model and control them using linear techniques. Consider the example of robotic systems, which are a combination of several mechanical and electrical components. Each mechanical or electrical component introduces a degree of nonlinearity, which is compounded because the components are interconnected in a complex configuration of serial and parallel connections.

Several nonlinear algorithms have been proposed in the literature to address the problem related to the modeling and control of robotic systems, e.g., Newton’s and quasi-newton’s methods, interior point, trust region, sequential quadratic programming, stochastic optimization, augmented Lagrangian, and penalty function are a few examples of such algorithms. Several derivative-free algorithms have also been introduced in the literature, such as evolutionary and genetic algorithms, particle swarm search (PSO), simulated annealing, etc. These algorithms have been applied to solve a wide variety of problems related to robots, e.g., kinematic and dynamic modeling, formulating control laws, task planning, path planning, sensor fusion, state estimation, etc., are just a few examples of problems in robotics solved using nonlinear optimization algorithms. Optimization algorithms have given way to several paradigms of control theory, e.g., optimal control, adaptive control, stochastic control, and impedance control. Needless to say, optimization algorithms are an integral component of robotic systems.

We are organizing this Special Issue to gather the latest research on nonlinear optimization and its applications in robotic modeling and control systems. It is out hope that the papers submitted in this SI will help to advance the research in the field of optimization and control.

Dr. Ameer Hamza Khan
Guest Editor

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• nonlinear optimization
• robotic control
• optimal control