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Abstract-We present a distributed control algorithm simultaneously solving both the stochastic target assignment and optimal motion control for large-scale swarms to achieve complex formation shapes. Our probabilistic swarm guidance using inhomogeneous Markov chains (PSG-IMC) algorithm adopts a Eulerian density-control framework, under which the physical space is partitioned into multiple bins and the swarm's density distribution over each bin is controlled in a probabilistic fashion to efficiently handle loss or the addition of agents. We assume that the number of agents is much larger than the number of bins and that each agent knows in which bin it is located, the desired formation shape, and the objective function and motion constraints. PSG-IMC determines the bin-to-bin transition probabilities of each agent using a time IMC. These time-varying Markov matrices are computed by each agent in real time using the feedback from the current swarm distribution, which is estimated in a distributed manner. The PSG-IMC algorithm minimizes the expected cost of transitions per time instant that are required to achieve and maintain the desired formation shape, even if agents are added to or removed from the swarm. PSG-IMC scales well with a large number of agents and complex formation shapes and can also be adapted for area exploration applications. We demonstrate the effectiveness of this proposed swarm guidance algorithm by using numerical simulations and hardware experiments with multiple quadrotors.

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This paper presents an attitude control strategy and a new nonlinear tracking controller for a spacecraft carrying a large object, such as an asteroid or a boulder. If the captured object is larger or comparable in size to the spacecraft and has significant modeling uncertainties, conventional nonlinear control laws that use exact feedforward cancellation are not suitable because they exhibit a large resultant disturbance torque. The proposed nonlinear tracking control law guarantees global exponential convergence of tracking errors with finite-gain L p stability in the presence of modeling uncertainties and disturbances, and it reduces the resultant disturbance torque. Furthermore, this control law permits the use of any attitude representation, and its integral control formulation eliminates any constant disturbance. Under small uncertainties, the best strategy for stabilizing the combined system is to track a fuel-optimal reference trajectory using this nonlinear control law because it consumes the least amount of fuel. In the presence of large uncertainties, the most effective strategy is to track the derivative plus proportional-derivativebased reference trajectory because it reduces the resultant disturbance torque. The effectiveness of the proposed attitude control methods is demonstrated by using results of numerical simulation based on an Asteroid Redirect Mission concept.