An optimal control approach for communication and motion co-optimization in realistic fading environments

We consider an energy co-optimization problem of minimizing the total communication and motion energy of a robot tasked with transmitting a given number of information bits while moving along a fixed path. The data is transmitted to a remote station over a fading channel, which changes along the trajectory of the robot. While a previous approach to the problem used a speed-based motion-energy model, this paper uses acceleration both as an input to the system and as a basis for the motion energy which is more realistic. Furthermore, while previous approaches posed the problem in discrete time, we formulate it in continuous time. This enables us to pose the problem in an optimal control framework amenable to the use of maximum principle. We then compute the optimal control input via an effective algorithm recently developed by us that converges very fast. We use practical models for channel fading and energy consumption: the channel quality is predicted based on actual measurements, and the energy models are based on physical principles. Simulation is used to solve a specific problem and demonstrate the efficacy of our proposed approach.