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In this paper, we aimed to study the energy consumption problem in a collaborative activity monitoring system (CAMS) that consists of a compan- ion robot and a wearable device. First, we tested the energy consumption in different operation modes of the system. Based on that, we analyzed the effect of band- width on the time cost and energy consumption which allowed us to combine WiFi and Bluetooth together for data transmission to improve the performance of the system. Second, we preprocessed the image data on the wearable device to reduce the size of images before sending them to the robot, and analyzed the time and energy consumption cost by local computing and data transmission. Third, based on the bandwidth of WiFi and Bluetooth, the requirement of time and energy consumption, we proposed an optimization problem on image sizes in which the wearable device decides how to send the data to the robot to reduce the energy and time cost. The results showed that the relations between the bandwidth, time cost, image resolutions and energy consumption could be used to improve the performance of CAMS.