Task Allocation of Heterogeneous Robots Under Temporal Logic Specifications With Inter-Task Constraints and Variable Capabilities

Multi-Robot task allocation (MRTA) exploits different capabilities of heterogeneous robots to facilitate collaborative tasks. However, existing works are mainly built on a key assumption that the robot capabilities are invariant and few consider variable capabilities (e.g., task-dependent or time-dependent capabilities). Besides, there may also exist a variety of inter-task constraints (e.g., unrelated tasks, compatible tasks, and exclusive tasks). Motivated by this practical need, we develop a novel task allocation framework for heterogeneous multi-robot systems with variable capabilities subject to inter-task constraints and temporal logic task specifications. Specifically, we extend conventional linear temporal logic (LTL) to capability LTL, namely $\boldsymbol {\mathrm {CaLT}\mathrm {L}^{\mathcal {T}}}$ , to describe heterogeneous multi-robots systems with variable capabilities and inter-task constraints. The Task Batch Planning Decision Tree Plus (TB- $\boldsymbol {\mathrm {PDT^{+}}}$ ) is then developed, which encodes the states of Büchi automaton, the system states, and the task process into a tree structure to represent the exploration progress. Based on the TB- $\boldsymbol {\mathrm {PDT^{+}}}$ , the Variable Capability and Inter-task Constraints Search (Var-CICS) is developed to find feasible task allocations and plans. Rigorous analysis shows that Var-CICS is valid (i.e., the generated task allocation is guaranteed to satisfy the task requirements) and complete (i.e., if a feasible task allocation exists, it is ensured to be found by Var-CICS). The complexity analysis also shows that the computation time of finding a satisfactory task allocation scales only quadratically with the number of automaton states, versus the exponential growth due to the product automaton in standard model checking methods. Numerical simulations and experiments demonstrate the effectiveness of Var-CICS. Note to Practitioners—Real-world applications often require a heterogeneous multi-robot system working collaboratively on a variety of tasks. Within such applications, robots can have diverse capabilities which may vary depending on the task at hand or over time, and are subject to inter-task constraints. Thus, in this work, we propose a new temporal logic to enrich the expressiveness in describing heterogeneous multi-robots systems with variable capabilities and inter-task constraints. We then develop the task batch planning decision tree plus and the variable capability and inter-task constraints search (Var-CICS) for the task allocation of heterogeneous multi-robot system. In contrast to automata-based methods, our method does not require sophisticated product automaton, which enables efficient and effective search of feasible task allocations. Furthermore, theoretical analyses show that Var-CICS is both complete and valid, while experimental results demonstrate its validity, efficiency and scalability.

I. Introduction

One of the ultimate goals of multi-robot systems is to collaborate for a wide range of tasks that cannot be completed by individual robots alone. Towards this goal, significant research effort has been devoted in multi-robot task allocation (MRTA) by exploiting different capabilities of the robots. However, existing works are mainly built on a key assumption that the robot capabilities are invariant and few considers variable capabilities (e.g., task-dependent or time-dependent capabilities). For example, as shown in Fig.1, assistive robots in the hospital may have multiple capabilities such as loading, disinfection, and virus-detection capabilities, which can be time-dependent or task-dependent. Besides variable capabilities, there may also exist a variety of inter-task constraints (e.g., unrelated tasks, compatible tasks, and exclusive tasks). For instance, the robots that have been to patient rooms are not allowed to visit the therapeutic department to avoid potential infection. Motivated by this practical need, this work aims to develop a task allocation framework for heterogeneous multi-robot systems with inter-task constraints and variable capabilities.Fig. 1.

The simulated hospital scenario. The tasks of visiting different patient rooms are considered as compatible while visiting the patient rooms is considered as exclusive with the task of visiting the therapeutic department due to potential infection. The robots are assumed to have different capabilities, such as the loading capability (i.e., an invariant capability), disinfection capability (i.e., a task-dependent capability), and virus-detection capability (i.e., a time-dependent capability). More explanations about the robot capabilities and the inter-task constraints are provided in Sec. III-B.