This paper explores a Deep Reinforcement Learning (DRL) approach for designing image-based control for edge robots to be implemented on Field Programmable Gate Arrays (FPGAs). Although FPGAs are more power-efficient than CPUs and GPUs, a typical DRL method cannot be applied since they are composed of many Logic Blocks (LBs) for high-speed logical operations but low-speed real-number operations. To cope with this problem, we propose a novel DRL algorithm called Binarized P-Network (BPN), which learns image-input control policies using Binarized Convolutional Neural Networks (BCNNs). To alleviate the instability of reinforcement learning caused by a BCNN with low function approximation accuracy, our BPN adopts a robust value update scheme called Conservative Value Iteration, which is tolerant of function approximation errors. We confirmed the BPN's effectiveness through applications to a visual tracking task in simulation and real-robot experiments with FPGA.