Soft Task Planning with Hierarchical Temporal Logic Specifications

This works exploits soft constraints in linear temporal logic task planning to enhance the agent’s capability in handling potentially conflicting or even infeasible tasks. Different from most existing works that focus on sticking to the original plan and trying to find a relaxed plan if the workspace does not permit, we augment the soft constraints to represent possible candidate sub-tasks that can be selected to fulfill the global task. Specifically, a hierarchical temporal logic specification is developed to represent LTL tasks with soft constraints and preferences. The hierarchical structure consists of an outer and inner layer, where the outer layer uses co- safe LTL to specify the task-level specifications and the inner layer specifies the low-level task-related atomic propositions via soft constraints. To cope with the hierarchical temporal logic specification, a hierarchical iterative search (HIS) algorithm is developed, which incrementally searches feasible atomic propositions and automaton states, and returns a task plan with minimum cost. Rigorous analysis shows that HIS based planning is feasible (i.e., the generated plan is applicable and satisfactory with respect to the task specification) and optimal (i.e, with minimum cost). Extensive simulation demonstrates the effectiveness of the proposed soft task planning approach.