Autonomous robot: Docking Robot

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Guillaume Lemaˆıtre Heriot-Watt University, Universitat de Girona, Universit´e de Bourgogne [email protected]

I. F ORMALIZATION First, we will formalize the different equations of the problem: A. Estimation motion p(Xt = is docked|Ut = DOCK IN T O ST AT ION, Xt−1 = is docked) = 0.9 p(Xt = is not docked|Ut = DOCK IN T O ST AT ION, Xt−1 = is docked) = 0.1 p(Xt = is docked|Ut = DOCK IN T O ST AT ION, Xt−1 = is not docked) = 0.8 p(Xt = is not docked|Ut = DOCK IN T O ST AT ION, Xt−1 = is not docked) = 0.2

B. Measurement p(Zt = ROBOT IS DOCKED|Xt = is docked) = 0.7 p(Zt = ROBOT IS DOCKED|Xt = is not docked) = 0.3 p(Zt = ROBOT IS N OT DOCKED|Xt = is not docked) = 0.6 p(Zt = ROBOT IS N OT DOCKED|Xt = is docked) = 0.4

II. A PPLICATION A. Prior belief ¯ (is docked) = p(X1 = is docked|Ut = DOCK IN T O ST AT ION, X0 = is docked)×(X0 = is docked)+ bef p(X1 = is docked|Ut = DOCK IN T O ST AT ION, X0 = is not docked) × (X0 = is not docked) = 0.9 × 0.5 + 0.8 × 0.5 = 0.85 ¯ (is not docked) = p(X1 = is not docked|Ut = DOCK IN T O ST AT ION, X0 = is docked) × (X0 = bef is docked) + p(X1 = is not docked|Ut = DOCK IN T O ST AT ION, X0 = is not docked) × (X0 = is not docked) = 0.1 × 0.5 + 0.2 × 0.5 = 0.15

B. Update and belief ¯ (is docked) = bel(X1 = is docked) = η × p(Z1 = ROBOT IS DOCKED|X1 = is docked) × bef η × 0.85 × 0.7 = η × 0.595 ¯ (is not docked) = bel(X1 = is not docked) = η×p(Z1 = ROBOT IS N OT DOCKED|X1 = is docked)×bef η × 0.15 × 0.4 = η × 0.06 1 = 1.5267 η = 0.595+0.06 Hence, bel(X1 = is docked) = 0.9084 bel(X1 = is not docked) = 0.0916