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.

Robust Counterexample-guided Optimization for Planning from Differentiable Temporal Logic

“…Our formulation differs from that presented in [4] and [5]; although both of these works seek to maximize the robustness margin ρ, neither consider the effect of disturbances χ. Our formulation is also distinct from the mixed-integer formulation in [2], since we consider ρ as part of an objective rather than as a constraint. Our unconstrained approach does not provide the same completeness guarantees as a mixed-integer constrained optimization (used in [2], [12], [13]), but empirical results in Section V demonstrate that our approach scales much better.…”

“…In addition, although the formal syntax of STL can seem opaque at first, it is often quite easy to translate STL formulae into readilyunderstood natural language. Due to its flexibility, STL is a common choice for specifying robotics problems such as trajectory planning [4], [5] and combined task and motion planning [2], [6], [7].…”

“…A number of classical methods exist for planning from STL specifications, the most common being abstraction-based methods [6], mixed-integer optimization-based methods [2], [8], and nonlinear optimization methods [4], [5], [9] (other approaches include sampling-based methods such as [10] and [11]). Abstraction-based methods have the longest history; these methods first construct a discrete abstraction (in the form of a graph or automaton) of the continuous state space, then plan over this discrete abstraction [6].…”

“…Unfortunately, although mixed-integer optimization is sound and complete, these mixed-integer programs quickly become intractable as the planning horizon increases [8], [12], [13]. Some works reduce the size of the program by using timed waypoints instead of a receding horizon [2], but this requires assumptions (such as access to a bounded-error tracking controller) that can be restrictive.…”

“…A significant gap in the state of the art is that existing optimization-based STL planners [2]- [5], [7], [9] do not explicitly consider the effects of environmental disturbances while planning. These approaches include some amount of robustness implicitly, typically by maximizing the margin by which a plan satisfies the STL specification, but this is often not sufficient in practice to prevent the plan from failing in response to small changes in the environment.…”