Figure 10.

Testing the control law with a predictive term, . (a,d) Typical time course of the beetle's angular velocity ω_b (grey line), the error angular velocity ω_e and the prey's angular velocity ω_p (both black lines). Data are from the chase shown in figure 6a. (b) Cross-correlation of the beetle's angular velocity ω_b and the prey error angular velocity ω_e. The correlation is the highest when τ = 0 ms (R² = 0.395 ± 0.233; n = 34). (c) Quantification for PD-control using the error angle θ_e and its derivative ω_e. The gains for each term in the control law, k₁ and k₂, were optimized for each value of τ by minimizing the RMS deviation δω_b as done previously for the proportional control law. The grey line shows the minimum deviation δω_b for the proportional control model. Adding the ω_e term does not improve the goodness of fit. (e) The cross-correlation function for the beetle's angular velocity ω_b and the prey's angular velocity ω_p has its maximum at a time delay of τ = 60 ms (R² = 0.679 ± 0.224; n = 34). (f) Quantification of models using both the positional error angle θ_e and the prey's angular velocity ω_p. The grey line represents the minimum deviation δω_b achieved by the proportional θ_e control model. Adding a velocity term improves the fit by 11.3%.