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In this article, we consider the problem of stabilizing a class of degenerate stochastic processes, which are constrained to a bounded Euclidean domain or a compact smooth manifold, to a given target probability density. This stabilization problem arises in the field of swarm robotics, for example, in applications where a swarm of robots is required to cover an area according to a target probability density. Most existing works on modeling and control of robotic swarms that use partial differential equation (PDE) models assume that the robots' dynamics are holonomic and, hence, the associated stochastic processes have generators that are elliptic. We relax this assumption on the ellipticity of the generator of the stochastic processes, and consider the more practical case of the stabilization problem for a swarm of agents whose dynamics are given by a controllable driftless control-affine system. We construct state-feedback control laws that exponentially stabilize a swarm of nonholonomic agents to a target probability density that is sufficiently regular. State-feedback laws can stabilize a swarm only to target probability densities that are positive everywhere. To stabilize the swarm to probability densities that possibly have disconnected supports, we introduce a semilinear PDE model of a collection of interacting agents governed by a hybrid switching diffusion process. The interaction between the agents is modeled using a (mean-field) feedback law that is a function of the local density of the swarm, with the switching parameters as the control inputs. We show that under the action of this feedback law, the semilinear PDE system is globally asymptotically stable about the given target probability density. The stabilization strategies with and without agent interactions are verified numerically for agents that evolve according to the Brockett integrator; the strategy with interactions is additionally verified for agents that evolve according to an underactuated s...
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Modeling Feasible Locomotion of Nanobots for Cancer Detection and Treatment
Deploying nanoscopic particles and robots in the human body promises increasingly selective drug delivery with fewer side effects. We consider the problem of a homogeneous swarm of nanobots locating a singular cancerous region and treating it by releasing some onboard payload of drugs once at the site. At nanoscale, the computation, communication, sensing, and locomotion capabilities of individual agents are extremely limited, noisy, and/or nonexistent. We present a general model to formally describe the individual and collective behaviour of agents in a colloidal environment, such as the bloodstream, for the problem of cancer detection and treatment by nanobots. This includes a feasible and precise model of agent locomotion, which is inspired by actual nanoscopic vesicles which, when in the presence of an external chemical gradient, tend towards areas of higher concentration by means of self-propulsion. The delivered payloads have a dual purpose of treating the cancer, as well as diffusing throughout the space to form a chemical gradient which other agents can sense and noisily ascend. We present simulation results to analyze the behavior of individual agents under our locomotion model and to investigate the efficacy of this collectively amplified chemical signal in helping the larger swarm efficiently locate the cancer site.
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- PAR ID:
- 10585735
- Publisher / Repository:
- 10th Workshop on Biological Distributed Algorithms (BDA)
- Date Published:
- Format(s):
- Medium: X
- Location:
- Nantes, France
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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