By Rod Mollise

*Cells and Robots* is an end result of the multidisciplinary examine extending over Biology, Robotics and Hybrid platforms concept. it really is encouraged through modeling reactive habit of the immune approach mobilephone inhabitants, the place each one phone is taken into account as an autonomous agent. In our modeling procedure, there's no distinction if the cells are obviously or artificially created brokers, comparable to robots. This appears to be like much more obvious once we introduce a case examine bearing on a large-size robot inhabitants situation. lower than this situation, we additionally formulate the optimum keep an eye on of maximizing the likelihood of robot presence in a given quarter and speak about the applying of the minimal precept for partial differential equations to this challenge. Simultaneous attention of telephone and robot populations is of mutual gain for Biology and Robotics, in addition to for the final realizing of multi-agent procedure 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, each year offered by way of the ecu Robotics examine community (EURON).

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**Additional resources for Cells and Robots: Modeling and Control of Large-Size Agent Populations**

**Example text**

Dt ⎥ ⎢ . D Theorems 1 and 2 relate to the dynamics of the CT M CμA state PDF. Theorem 1 is of special importance. Given an initial state PDF, we can use the theorem to predict the state PDF evolution. In the case of the CT M CμA T-cell population model, this theorem can be used to predict the TCR distribution over the T-cell population. It enables us to test diﬀerent hypotheses about the T-cell micro-dynamics against experimental data, using a mathematical model. Although the state PDF contains the complete information about population measurements, the experimental test can only be made using the Micro-Agent output PDF η(y, t).

T ⎥ ⎢ . 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.

29) which is the Liouville equation. 2) is the vector of time functions representing the time evolution of the CT M CμA state PDF. To solve this equation, the region of interest Ω ∈ X and boundary condition should be deﬁned [20]. An example of the boundary condition is ρ(x, t) = 0 for all x ∈ ∂Ω. 2) and can strongly inﬂuence the solution [20]. Numerical methods for solving this type of equation are discussed in [85]. The following theorem focuses on is about the time derivatives of the PDE solution: Theorem 2.