[S19] Modern Control Paradigms

The course helps students systematically explore several topics and research directions of modern

robotics and nonlinear control theory linked to efforts in developing scalable methods for performing and

analyzing agile movements of dynamically constrained robotic systems. Demands for automating

various labor-intensive tasks such as grasping, manipulating or handling of external objects (performed

nowadays in industry and service applications primarily by humans) motivate for model-based motion

planning and control methods for such systems. Similarly, dynamic and actuation constraints are

dominating in developing aggressive maneuvers for flying machines; they are important for searching

and controlling gaits of walking robots etc.


Most of dynamic constraints in applications are case specific or linked to scenarios of work of

mechanisms. Meanwhile, some constraints are generic and can be simultaneously present in describing

behaviors of quite distant nonlinear systems. Constraints due to underactuation provide examples of

such generic structural features of nonlinear mechanical systems. They appear due to system designs

and literally mean an excess of a number of degrees of freedom of the system (that are representative

for a searched movement) over a number of actuators available in the system (for performing the

movement). For a nonlinear mechanical system, the Newton second law describing the dynamics of

non-actuated variables can be interpreted as a dynamic constraint defining a continuum set of equalities,

which a movement of the system must obey and which are parameterized by a time interval the motion

is defined. Such non-integrable relations can be irrelevant for some tasks. For instance, underactuation

constraints in regulating a position of a drone might locally have a negligible effect. Meanwhile, the

constraints are dominant and should be taken into account in planning and performing its agile

maneuvers.


The lectures provide introductory materials and problem settings to the subject exploiting generic

arguments for modelling, representing and analyzing behaviors of nonlinear systems, which can be

further extended and applied for controlled mechanical systems. The development is well illustrated by

solving a number of comprehensive examples of increased complexity, where important mathematical

concepts and tools are emphasized and exemplified. The common thread of the lectures is put on

discussion of formalization of motion planning, stabilization and stability analysis assignments and on

discussion of integrated approaches for solving the tasks, which are relevant to engineering applications

and practice. To the end, one of lectures is devoted to the analysis and control system design for the

robotic system developed for performing non-prehensile manipulation tasks (the Butterfly robot).