Backed by the virtually unbounded resources of the cloud, battery-powered mobile robotics can also benefit from cloud computing, meeting the demands of even the most computationally and resource-intensive tasks. However, many existing mobile-cloud hybrid (MCH) robotic tasks are inefficient in terms of optimizing trade-offs between simultaneously conflicting objectives, such as minimizing both battery power consumption and network usage. To tackle this problem we propose a novel approach that can be used not only to instrument an MCH robotic task but also to search for its efficient configurations representing compromise solution between the objectives. We introduce a general-purpose MCH framework to measure, at runtime, how well the tasks meet these two objectives. The framework employs these efficient configurations to make decisions at runtime, which are based on: (1) changing of the environment (i.e., WiFi signal level variation), and (2) itself in a changing environment (i.e., actual observed packet loss in the network). Also, we introduce a novel search-based multi-objective optimization (MOO) algorithm, which works in two steps to search for efficient configurations of MCH applications. Analysis of our results shows that: (i) using self-adaptive and self-aware decisions, an MCH foraging task performed by a battery-powered robot can achieve better optimization in a changing environment than using static offloading or running the task only on the robot. However, a self-adaptive decision would fall behind when the change in the environment happens within the system. In such a case, a self-aware system can perform well, in terms of minimizing the two objectives. (ii) The Two-Step algorithm can search for better quality configurations for MCH robotic tasks of having a size from small to medium scale, in terms of the total number of their offloadable modules.