Jeremy Klotz

Jeremy Klotz, Shree K. Nayar

Solar panels are increasingly deployed in cities on rooftops, walls, and urban infrastructure. Although the panel costs have fallen in recent years, the soft costs of installing them have not. These soft costs include assessing the illumination (irradiance) of a panel, which is typically performed using a 3D model that fails to capture small nearby structures that impact the irradiance. Our approach uses a single image taken at the panel's location to forecast its irradiance at any time in the future. We use visual cues in the image to find the camera's orientation and the portion of the sky visible to the panel in order to forecast the irradiance due to the sun and the sky. In addition, we show that the irradiance due to reflections from nearby buildings varies smoothly over time and can be forecasted from the image. This approach enables assessing the solar energy potential of any surface and forecasting the temporal variation of a panel's irradiance. We validate our approach using real irradiance measurements in urban canyons. We show that our approach often yields more accurate irradiance forecasts compared to conventional irradiance-based transposition methods and 3D model-based simulations. We also show that a single spherical image can be used to find the best fixed orientation of a panel. Finally, we present Solaris, a device to capture the image seen by a panel in a variety of urban settings.

Francesco Pasti, Jeremy Klotz, Nicola Bellotto et al.

Visual-Inertial Odometry(VIO), which is critical to mobile robot navigation, uses cameras with a large number of pixels. Capturing and processing camera images requires significant resources. This work presents a minimalist approach to planar odometry, demonstrating that just four visual measurements and an IMU can provide robust motion estimation for differential-drive robots. Our key insight is that four downward-facing photodiodes that sense the world through optical Gabor masks produce signals that encode speed. Based on this, we jointly optimize the mask parameters alongside a Temporal Convolutional Network (TCN) using a physically-grounded simulator. The resulting model decodes speed from just the four measurements produced by the photodiodes. Pairing these estimates with the angular speed from an IMU yields a continuous planar trajectory. We validate our approach with a prototype sensor mounted on a differential drive robot. Across diverse indoor and outdoor terrains, our system closely tracks the reference ground truth without any real-world fine-tuning. Our work shows that minimalist sensing enables efficient and accurate planar odometry.

Jeremy Klotz, Shree K. Nayar

A minimalist vision system uses the smallest number of pixels needed to solve a vision task. While traditional cameras use a large grid of square pixels, a minimalist camera uses freeform pixels that can take on arbitrary shapes to increase their information content. We show that the hardware of a minimalist camera can be modeled as the first layer of a neural network, where the subsequent layers are used for inference. Training the network for any given task yields the shapes of the camera's freeform pixels, each of which is implemented using a photodetector and an optical mask. We have designed minimalist cameras for monitoring indoor spaces (with 8 pixels), measuring room lighting (with 8 pixels), and estimating traffic flow (with 8 pixels). The performance demonstrated by these systems is on par with a traditional camera with orders of magnitude more pixels. Minimalist vision has two major advantages. First, it naturally tends to preserve the privacy of individuals in the scene since the captured information is inadequate for extracting visual details. Second, since the number of measurements made by a minimalist camera is very small, we show that it can be fully self-powered, i.e., function without an external power supply or a battery.

Shree K. Nayar, Jeremy Klotz, Nikhil Nanda et al.

We present a sensor that can measure light and wirelessly communicate the measurement, without the need for an external power source or a battery. Our sensor, called cricket, harvests energy from incident light. It is asleep for most of the time and transmits a short and strong radio frequency chirp when its harvested energy reaches a specific level. The carrier frequency of each cricket is fixed and reveals its identity, and the duration between consecutive chirps is a measure of the incident light level. We have characterized the radiometric response function, signal-to-noise ratio and dynamic range of cricket. We have experimentally verified that cricket can be miniaturized at the expense of increasing the duration between chirps. We show that a cube with a cricket on each of its sides can be used to estimate the centroid of any complex illumination, which has value in applications such as solar tracking. We also demonstrate the use of crickets for creating untethered sensor arrays that can produce video and control lighting for energy conservation. Finally, we modified cricket's circuit to develop battery-free electronic sunglasses that can instantly adapt to environmental illumination.

Jeremy Klotz, Shree K. Nayar

A solar panel harvests the most energy when pointing in the direction that maximizes the total illumination (irradiance) falling on it. Given an arbitrary panel orientation and an arbitrary environmental illumination, we address the problem of finding the direction of maximum total irradiance. We develop a minimal sensing approach where measurements from just four photodetectors are used to iteratively vary the tilt of the panel to maximize the irradiance. Many environments produce irradiance functions with multiple local maxima. As a result, simply measuring the gradient of the irradiance function and applying gradient ascent will not work. We show that a larger, optimized tilt between the detectors and the panel is equivalent to blurring the irradiance function. This has the effect of eliminating local maxima and turning the irradiance function into a unimodal one, whose maximum can be found using gradient ascent. We show that there is a close relationship between our approach and scale space theory. We collected a large dataset of high-dynamic range lighting environments in Manhattan, called UrbanSky. We use this dataset to conduct simulations to verify the robustness of our approach. Next, we simulate the energy harvested using our approach under dynamic illumination. Finally, we built a portable solar panel with four compact detectors and an actuator to conduct experiments in various real-world settings: direct sunlight, cloudy sky, urban settings with occlusions and shadows, and complex indoor lighting. In all cases, we show improvements in harvested energy compared to standard approaches for orienting a solar panel.