Multi-agent Motion Planning from Signal Temporal Logic Specifications

Abstract

We tackle the challenging problem of multi-agent cooperative motion planning for complex tasks described using signal temporal logic (STL), where robots can have nonlinear and nonholonomic dynamics. Existing methods in multi-agent motion planning, especially those based on discrete abstractions and model predictive control (MPC), suffer from limited scalability with respect to the complexity of the task, the size of the workspace, and the planning horizon. We present a method based on timed waypoints to address this issue. We show that timed waypoints can help abstract nonlinear behaviors of the system as safety envelopes around the reference path defined by those waypoints. Then the search for waypoints satisfying the STL specifications can be inductively encoded as a mixedinteger linear program. The agents following the synthesized timed waypoints have their tasks automatically allocated, and are guaranteed to satisfy the STL specifications while avoiding collisions. We evaluate the algorithm on a wide variety of benchmarks. Results show that it supports multi-agent planning from complex specification over long planning horizons, and significantly outperforms state-of-the-art abstraction-based and MPC-based motion planning methods. The implementation is available at https://github.com/sundw2014/STLPlanning.

Mixed-Integer Programming for Signal Temporal Logic with Fewer Binary Variables

“…Remark 1. This syntax is slightly more general than that with linear predicates only, as considered in [9]- [12], since such convex predicates include linear ones g π (y t ) = a T y − b. Note that negation (¬) can be applied to linear predicates, but not to more general convex predicates such as ellipses.…”

“…where T j i denotes the j th target in group i. The final scenario is inspired by [12], [25], and requires the robot to collect keys (i.e., visit blue regions) associated with certain doors (red) before reaching an end goal (green). This specification can be written as…”

“…For example, rewriting formulas in Positive Normal Form (PNF) significantly reduces the number of binary variables and constraints [8], [11]. Waypointbased abstractions can further limit the problem size [12]. Another possibility is to formulate MICPs with tighter convex relaxations.…”

Event-Based Signal Temporal Logic Synthesis for Single and Multi-Robot Tasks

“…These methods are useful in that they provide guarantees on the satisfaction of a specification over the prediction horizon, but they do not scale to long time horizons or complex specifications, due to the increase in decision variables. Other MILP solutions to synthesizing control satisfying STL specifications [13], [14] attempt to improve the computational efficiency by decomposing the specification into subtasks or waypoints. Work from [15] provide methods to satisfy STL specifications using Mixed-integer Convex Programming while reducing the number of binary decision variables in the optimization problem.…”

“…Using existing methods such as MPC [7], [10]- [12] or MILP solutions [13], [14], one can update the specification; however, the new specification would initiate re-synthesis and, as stated above, this is a computationally inefficient. In our work, we provide an efficient solution to modify tasks online without the need to stop or pause execution, in most cases; we discuss computation limitations that require execution to pause for large specification modifications.…”