Time-bounded planning with uncertain task duration distributions

Abstract

We consider planning problems where a robot must gather reward by completing tasks at each of a large set of locations while constrained by a time bound. Our focus is problems where the context under which each task will be executed can be predicted, but is not known in advance. Here, the term context refers to the conditions under which the task is executed, and can be related to the robot’s internal state (e.g., how well it is localised?), or the environment itself (e.g., how dirty is the floor the robot must clean?). This context has an impact on the time required to execute the task, which we model probabilistically. We model the problem of time-bounded planning for tasks executed under uncertain contexts as a Markov decision process with discrete time in the state, and propose variants on this model which allow adaptation to different robotics domains. Due to the intractability of the general model, we propose simplifications to allow planning in large domains. The key idea behind these simplifications is constraining navigation using a solution to the travelling salesperson problem. We evaluate our models on maps generated from real-world environments and consider two domains with different characteristics: UV disinfection, and cleaning. We evaluate the effect of model variants and simplifications on performance, and show that policies obtained for our models outperform a rule-based baseline, as well as a model which does not consider context. We also evaluate our models in a real robot experiment where a quadruped performs simulated inspection tasks in an industrial environment.