The potential impact of autonomous robots on everyday life is evident in emerging applications such as precision agriculture, search and rescue, and infrastructure inspection. However, such applications necessitate operation in unknown and unstructured environments with a broad and sophisticated set of objectives, all under strict computation and power limitations. We therefore argue that the computational kernels enabling robotic autonomy must be scheduled and optimized to guarantee timely and correct behavior, while allowing for reconfiguration of scheduling parameters at runtime. In this paper, we consider a necessary first step towards this goal of computational awareness in autonomous robots: an empirical study of a base set of computational kernels from the resource management perspective. Specifically, we conduct a datadriven study of the timing, power, and memory performance of kernels for localization and mapping, path planning, task allocation, depth estimation, and optical flow, across three embedded computing platforms. We profile and analyze these kernels to provide insight into scheduling and dynamic resource management for computation-aware autonomous robots. Notably, our results show that there is a correlation of kernel performance with a robot's operational environment, justifying the notion of computation-aware robots and why our work is a crucial step towards this goal.