Control through Constraint

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Recently multi-agent navigation robots have been gaining increasing popularity indiverse applications such as agriculture, package delivery, exploration, search and rescue due to their maneuverability and collaborativity. The control algorithm is the nucleus of such intelligent and autonomous robots performing tasks. In real-world applications, the robots are subjected to nonlinear dynamics, external disturbances, actuator saturation/dynamics, and modeling, estimation, and measurement errors. Furthermore, teams of robots are needed to perform collaboratively while ensuring inter-robot and robot-obstacle collision avoidance.

To address these needs, a novel control paradigm has been developed for multiagent navigation robots that possesses safety, robustness, resilience, scalability, and computation efficiency. The control rule is fully defined by the current active subset of a superset of inequality constraints, which contrasts methods of minimizing a weighted cost function subject to stability constraints. The advantages of this method are that

• the constraints (equality, inequality, holonomic, nonholonomic, scleronomic, rheonomic, etc.) can be handled without trying to \look ahead" to a finite time horizon;• the nonlinear control actions are specified by instantly solving a linear matrix equation; • it does not involve a cost function; • it does not involve any dynamics linearization; • the control parameters are physically interpretable; • actuator saturation and actuator dynamics are readily incorporated; and • it is applicable to fully nonlinear, time-varying, and/or arbitrary-order dynamical systems; and • it can simultaneously control the position and orientation of mechanical systems in one unified step.

These features are achieved through a novel generalization of Gauss’s Principleof Least Constraint (GPLC). GPLC was originally conceived to incorporate hard equality constraints into second-order dynamical systems. The contribution of this dissertation is to define the control actions from the Lagrange multipliers associated with inequality constraints (e.g., collision avoidance constraints) and to accommodate dynamical systems of any order. Thus, the constrained equations of motion are expressed as a Karush-Kuhn-Tucker (KKT) system (a linear matrix equation), which is solved without iteration at each time step.

This constraint-based control has been applied to the navigation control of multiagent, multi-swarm systems of double integrators, fully nonlinear quadrotor drones, and nonholonomic, differential drive, wheeled mobile robots subjected to actuator saturation, actuator dynamics, and external disturbances. Two types of constraints are considered for the aforementioned three types of systems: path following and collision avoidance constraints. Each constraint can be formulated based on vector norms or vector components and can be in either equality or inequality format. Thevector-component-based collision constraints lead to a natural byproduct of resolving deadlock in navigating swarms. Furthermore, through a partition of collision avoidance constraints among colliding agents, the control architecture for the navigation swarms can be centralized or decentralized. Numerical studies on swarms of double integrators, nonlinear quadrotor drones, and nonholonomic wheeled mobile robots have demonstrated the effectiveness and efficiency of the proposed approach.





Zhang, Boyang (2023). Control through Constraint. Dissertation, Duke University. Retrieved from


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