Relaxed Constraints in Gauss s Principle for High Speed, Large Scale, Multi-Agent Network Dynamics
Abstract
A physically-motivated, mathematical framework for the high-speed control of individual agents within a swarm is proposed in order to meet the three requirements of swarm dynamics: path following, aggregation, and collision avoidance. These goals are achieved by representing the equation of motion for each agent as the unique minimum of a quadratic objective subject to relaxed (linear inequality) constraints. The formulation may be applied to a single swarm tracking a trajectory, the crossing of multiple swarms, and the control of independent swarms maneuvering around static or dynamic obstacles. This abstraction enables solutions to a number of heretofore unanswered challenges in the control of multi-agent swarms, namely, how to recover from constraint violations, and how to ensure resiliency to the kinds of exogenous actions (environmental and potentially adversarial) that are ubiquitous in the physical world. This formulation also allows the incorporation of actuator delay, actuator saturation, and vehicle dynamics. The objective of the proposed research will be to demonstrate the versatility and robustness of this relaxed-constraint approach to the control of swarming agents, in the presence of moving obstacles and exogenous actions, and with agents that may be underactuated or otherwise electro-mechanically constrained. Currently, simultaneous modeling of actuator dynamics, vehicle dynamics, resiliency to constraint violations, rejection of realistic exogenous disturbances and state estimation errors are underrepresented in the literature. The proposed work will extend the state-of-the-art on multi-agent systems control by introducing a computationally efficient (e.g., without requiring a continual updating of finite-horizon optimizations) general nonlinear constrained feedback control methodology that will be demonstrably robust to exogenous disturbances and capable controlling dense multi-agent systems safely at high-speeds. In essence, the proposed approach extends Gauss s minimization principle by relaxing the constraints that define swarm dynamics and by strictly enforcing the asymptotic convergence of each violated constraint to feasible coordinates. So doing, the asymptotic convergence of the out-of-equilibrium dynamics to the admissible manifold are strictly enforced. The feedback control rule involves the minimization of a linearly-constrained quadratic objective at each time step, in which the active constraints change in time. With large and dense multi-agent systems, the number of active constraints can approach the number of dynamic coordinates and these constraints can be potentially linearly dependent (to within machine precision). This situation is easily overcome by regularizing a subspace of the matrix equations, or, more precisely, by computing a linear independent subspace of the constraints, and representing the dependent constraints within this basis. The proposed research tasks include the development of a decentralized formulation of this technique, the incorporation of underactuated vehicle dynamics, the incorporation of non-stationary exogenous disturbances, and the assessment of robustness to state estimation errors. Results will be demonstrated in a probabilistic context, by adapting the method to maximize the speed of specific complex maneuvers subject to a constraint on minimizing the probability of agent-to-agent collisions.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 06, 2019
- Source ID
- W911NF1910410
Entities
People
- Henri P. Gavin
Organizations
- Army Contracting Command
- Duke University
- United States Army