Energy efficiency is a fundamental goal in robotic control. Various components within a robot, such as mechanical systems, computational units, and sensors, consume energy, all powered by the battery unit. Each component features several actuators and individual controllers that optimize energy usage locally, often without regard to one another. In this paper, we highlight a significant phenomenon indicating a considerable dependency between the mechanical and computational parts of the robot as energy consumers and the battery state of charge (SOC) as the energy provider. We demonstrate that as the battery SOC fluctuates, the behavior of energy consumption also varies, necessitating a unified controller with awareness of this relationship. Motivated by this observation, we propose a battery-aware co-optimization strategy for the mechanical and computational units, leveraging configuration space exploration to optimize the motor speed and the CPU frequency under different environmental conditions and battery SOC levels. Experimental results demonstrate the effectiveness of our approach in extending the operational lifetime of a robot under varying battery SOC and workload conditions, enhancing the energy efficiency of a case study rover by up to 53.93% w.r.t. selected baselines and similar past approaches.