Tuning movement for sensing in an uncertain world
- Center for Robotics and Biosystems, Northwestern University, United States
- Department of Biomedical Engineering, Northwestern University, United States
- Department of Mechanical Engineering, Northwestern University, United States
- Department of Neurobiology, Northwestern University, United States
Figures
Figure 1 with 1 supplement
Illustration of a 2-D expected information density, information maximization and energy-constrained proportional betting.
(A) The heat map represents the expected information density. Because the peak expected information is typically not at the same location as the object, we illustrate the target peak as the point of …
Figure 1—figure supplement 1
Whole-body or sensory organ small-amplitude motions are ubiquitous as animals track targets.
Here we show siphon casting behavior in the marine snail (body, Ferner and Weissburg, 2005), cross-current swimming in the Chambered nautilus (body, Basil et al., 2000), whole-body oscillations in …
Figure 2 with 3 supplements
Longitudinal refuge tracking behavior in weakly electric fish and core components of EIH.
(A) Head-on view of experimental apparatus. A computer-controlled linear servo moves the refuge forward and backward along the longitudinal axis of the fish. Jamming electrodes are mounted to the …
Figure 2—figure supplement 1
Single target tracking simulation with EIH and infotaxis in the presence of a simulated physical distractor.
In this simulation, a single target and a physical distractor coexist in the workspace. The simulated physical distractor has a different observation model that leads to a different measurement …
Figure 2—figure supplement 2
Dual target tracking simulation with EIH and infotaxis.
In this simulation, two identical targets (with the same observation model) are present in the workspace, indicated by the two blue lines. To help visualize the outcome, the belief (left panel) and …
Figure 2—figure supplement 3
Effect of jamming and how it varies with jamming intensity.
(A) A representative trial of how a fish’s electric organ discharge (EOD) frequency shifts up continuously as the jamming signal is being applied. The area shaded with light blue indicates when …
Figure 3
Fish behavior versus EIH predictions.
(A) Relative exploration values (defined in text) for the fish and EIH trajectories under strong and weak signal conditions. Each dot represents a behavioral trial or simulation. EIH (bottom row) …
Figure 4 with 1 supplement
Sensing-related movements reduce tracking error.
The full-body oscillation in the simulated EIH weak signal sensor trajectory (similar to Figure 2H) was gradually removed through stepped increases of attenuation over the sensing-related movement …
Figure 4—figure supplement 1
How sensing-related movements were attenuated for analyzing the impact of their diminishment.
(A) Response of three types of sensing-related movement attenuation filters. We used an IIR lowpass filter with a cutoff frequency of 0.2 Hz to avoid filtering the baseline tracking frequency band …
Figure 5
Relative energy for electric fish tracking behavior and EIH-generated behavior with attenuated body oscillations.
(A) Relative energy (definition: text) used by the electric fish during refuge tracking behavior under strong and weak signal conditions. Trials are similar to those shown in Figure 2C–D. Weak …
Figure 6 with 5 supplements
Trajectory comparison of animals tracking a target compared to EIH, and relative exploration across all trials.
Three representative live animal trajectories above trajectories generated by the EIH algorithm, with their duration cropped for visual clarity. The moth data is not shown here due to the complexity …
Figure 6—figure supplement 1
Systematic comparison between EIH and infotaxis in tracking a sinusoidally moving target.
Simulations of a sensor tracking a target moving sinusoidally under 17 different SNR conditions from 10 dB to 55 dB. For each SNR condition, 10 simulations with different pseudo-number seeds are …
Figure 6—figure supplement 2
Rat odor tracking behavior and EIH simulation.
In a prior study (Khan et al., 2012), Wistar rats (Rattus norvegicus, Berkenhout 1769) performed an odor tracking task by following a uniform odor trail on a moving treadmill with only olfactory …
Figure 6—figure supplement 3
Evolution of belief over time for the trials shown in Figure 6.
EIH simulations of tracking behavior of weakly electric fish, mole, and cockroach. The trials shown are identical to those shown in Figure 6. Simulated sensor position over time is the solid green …
Figure 6—figure supplement 4
Sensitivity analysis on the ratio between control cost and ergodic cost in the objective function of trajectory optimization.
Simulations are conducted in the same way as Figure 6—figure supplement 1 but only for a fixed SNR under weak signal conditions (20 dB). The control cost prefactor R is varied while fixing the …
Figure 6—figure supplement 5
Measurements compared to prediction of EIH in two conditions where an animal needs to find the signal during tracking behavior.
As a demonstration of how our model seamlessly transitions between exploitation and exploration, we examined an instance in the measured behavior of the live animals in which the rat appears to lose …
Figure 7
Spectral analysis of live animal behavior and simulated behavior.
All the single trial Fourier spectra shown in A-B, E-F, and I-J are for the trials shown in Figure 6. (A–B) The already shown spectral analysis of the fish tracking data is included here for …
Videos
Video 1
Segments of behavior across the four species analyzed.
Video 2
The ergodic information harvesting algorithm applied to stationary object localization in a bio-inspired electrolocation robot.
Tables
Table 1
Parameters of EIH Simulation.
| Parameter | Symbol | Value | Source and note |
|---|---|---|---|
| Variance of observation model | 0.06 | is initially chosen to fit weakly electric fish behavior and kept the same for all the sensory modalities simulated for the sake of model consistency | |
| Time step of the simulation | 0.025, 0.005 | In seconds. is initially chosen to fit weakly electric fish behavior and fixed for all the EIH and infotaxis simulations except for moth, where is set to 0.005 s to account for the higher velocity of the sum-of-sine trajectory | |
| Duration of planned trajectory | T | 2.5, 0.5 | In seconds. T is initially chosen to fit weakly electric fish behavior and kept the same for all the EIH simulations except for moth, where T is set to 0.5 to account for the higher velocity of the sum-of-sine trajectory |
| Step size control of the backtracking line search of trajectory optimization | 0.1 | and are picked to balance between the speed of convergence and the final cost of the trajectory optimization and are fixed across all the EIH simulations | |
| Step size control of the backtracking line search of trajectory optimization | 0.4 | and are picked to balance between the speed of convergence and the final cost of the trajectory optimization and are fixed across all the EIH simulations | |
| Weight of the distance from ergodicity term in the cost function of trajectory optimization loop (see Algorithm 1) | 5 | is initially chosen to fit weakly electric fish behavior and kept the same for all the simulations. Note that changing changes the trade-off between distance from ergodicity (how much information one wants) and control effort (how much energy one is willing to give up). As a result, there is mild sensitivity to this parameter—making it an order of magnitude larger will lead to a more exploratory trajectory while making it an order of magnitude smaller will lead to less exploration. If is set to zero, no movement will occur at all. For further discussion of this point, see Miller et al., 2016. Finally, a sensitivity analysis is also provided in Figure 6—figure supplement 4 | |
| Weight of the control term in the cost function of trajectory optimization loop (see Algorithm 1) | R | 10, 20 | R is initially chosen to fit weakly electric fish behavior and kept the same for all the simulations except for moth, where R is set to 20 since otherwise, the simulated moth body moves faster than the measured data due to the decrease in T from 2.5 to 0.5. Note that the control cost is equivalent to the total kinetic energy required to execute the candidate trajectory given our assumption of a unit point-mass body |
| Number of dimensions used for Sobolev space norm in ergodic metric | 15 | is initially chosen to be a sufficient number for representing all the behavioral data considered in this paper and kept the same for all the simulations | |
| Initial control input | 0 | Zero control is applied at the beginning of every simulation | |
| Initial belief | Initial belief is set and fixed to a uniform (“flat”) prior distribution within the workspace (from 0 to 1) where the probability of the target being at every location is identical |
Table 2
Simulation parameters used for each figure.
| Figure | Category | SNR (dB) | Initial position | Target trajectory | Biological condition |
|---|---|---|---|---|---|
| Figure 1E | Weak Signal | ≤30 | 0.7 | Sinusoid | N/A (simulation) |
| Figure 1F | Strong Signal | ≥50 | 0.7 | Sinusoid | N/A (simulation) |
| Figure 2G,I and 3A-C | Weak Signal | ≤30 | 0.4 | Sinusoid | N/A (simulation) |
| Figure 2F,H and 3A-C | Strong Signal | ≥50 | 0.4 | Sinusoid | N/A (simulation) |
| Figure 2—figure supplement 1 | Weak Signal | ≤30 | 0.4 | Stationary | N/A (simulation) |
| Figure 2—figure supplement 2 | Weak Signal | ≤30 | 0.4 | Stationary | N/A (simulation) |
| Figure 4A–C and Figure 5B | Weak Signal | ≤30 | 0.4 | Sinusoid | N/A (simulation) |
| Figure 6A and Figure 7B,D | Strong Signal | ≥50 | 0.4 | Sinusoid | No jamming |
| Figure 6A and Figure 7B,D | Weak Signal | ≤30 | 0.4 | Sinusoid | mA jamming |
| Figure 6B and 7F,H | Strong Signal | ≥50 | 0.2 | Stationary | Intact control |
| Figure 6B and 7F,H | Weak Signal | ≤30 | 0.6 | Stationary | Single-side nostril block and crossed airflow |
| Figure 6C and 7J,L | Strong Signal | ≥50 | 0.475 | Stationary | 4 mm intact antenna |
| Figure 6C and 7J,L | Weak Signal | ≤30 | 0.4 | Stationary | 1 and 2 mm bilaterally trimmed antenna |
| Figure 6—figure supplement 1 | Strong and Weak Signal | 10–55 | 0.4 | Sinusoid | N/A (simulation) |
| Figure 6—figure supplement 2 | Strong Signal | ≥50 | 0.8 | Prescribed by study (Khan et al., 2012) | Sham stitching |
| Figure 6—figure supplement 2 | Weak Signal | ≤30 | 0.3 | Prescribed by study (Khan et al., 2012) | Single-side nostril stitching |
| Figure 6—figure supplement 3 | Strong Signal | ≥50 | 0.4 | Sinusoid | N/A (simulation) |
| Figure 6—figure supplement 3 | Weak Signal | ≤30 | 0.4 | Sinusoid | N/A (simulation) |
| Figure 6—figure supplement 4 | Weak Signal | 20 | 0.4 | Sinusoid | N/A (simulation) |
| Figure 6—figure supplement 5A | Weak Signal | ≤30 | 0.9 | Prescribed by study (Khan et al., 2012) | Single-side nostril stitching |
| Figure 6—figure supplement 5B | Weak Signal | ≤30 | 0.45 | Stationary | Single-side nostril block |
| Figure 7N,P | Strong Signal | ≥50 | 0.4 | Prescribed by study (Stöckl et al., 2017) | 3000 lux ‘high-light’ |
| Figure 7N,P | Weak Signal | ≤30 | 0.4 | Prescribed by study (Stöckl et al., 2017) | 15 lux ‘low-light’ |
