By Dejan Lj. Milutinovic, Pedro U. Lima
Cells and Robots is an consequence of the multidisciplinary learn extending over Biology, Robotics and Hybrid structures concept. it's encouraged via modeling reactive habit of the immune procedure mobilephone inhabitants, the place every one mobilephone is taken into account as an autonomous agent.
In our modeling strategy, there's no distinction if the cells are obviously or artificially created brokers, corresponding to robots. This appears to be like much more obtrusive after we introduce a case learn bearing on a large-size robot inhabitants situation. below this situation, we additionally formulate the optimum regulate of maximizing the likelihood of robot presence in a given sector and speak about the applying of the minimal precept for partial differential equations to this challenge. Simultaneous attention of cellphone and robot populations is of mutual profit for Biology and Robotics, in addition to for the overall knowing of multi-agent process dynamics.
The textual content of this monograph relies at the PhD thesis of the 1st writer. The paintings was once a runner-up for the 5th version of the Georges Giralt Award for the simplest eu PhD thesis in Robotics, every year offered via the ecu Robotics learn community (EURON).
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Extra info for Cells and Robots: Modeling and Control of Large-Size Agent Populations (Springer Tracts in Advanced Robotics)
6) 28 4. Micro-Agent Population Dynamics Fig. 1. Micro-Agent state space: xk -kth dimension of the continuous state space, q-discrete state, fi (x)-vector field at x ∈ X for q = i, V -trajectory volume and fij (x) is the jth component of vector field fi (x) at state (x, i), x ∈ X, X = Rn ,i = 1, 2, . . N . [end of theorem] Proof. 1. By xk , we denote the kth dimension of the continuous state space X, q is the discrete state space and fi (x) is the vector field at x ∈ X for the discrete state q = i.
In this modeling approach, we assume that motion dynamics produces the time sequence of the events u(t) which changes the discrete state of the T-cell. This time event sequence is defined at each time instant and takes value a, b or ε. The symbol a and b stands for conjugate f ormation and conjugate dissociation event respectively. Symbol ε is introduced to describe no event, which means that the discrete state is not changing. The discrete states are introduced to model different TCR expression variations of the T-cell, when the T-cell is conjugated to APC or free.
In the formulation of the answer, we are using the PDF of the Micro-Agent state because it is a way to preserve the complete information about the dynamical system state. Using this (complete) information, any kind of the population macro-measurements can be calculated. The proposed answer is: The individual Micro-Agent dynamics and the dynamics of the MicroAgents population measurements are linked through the probability density function of the Micro-Agent state in that population. Although this answer is of a philosophical nature, it provides us with the intuition on how to look for a mathematically tractable answer.