Motion planning in dynamic environments with bounded time temporal logic specifications

Abstract

In this paper, we consider the problem of robotic motion planning that satisfies some bounded time high level specifications. Although temporal logic can efficiently express high level specifications such as coverage, obstacle avoidance, temporal ordering of tasks etc., it fails to address problems with explicit timing constraints. The inherent limitations of Linear Temporal Logic (LTL) to address problems with explicit timing constraints have been overcome by translating the planning problem from the workspace of the robot to a higher dimensional space called spacetime where the existing LTL semantics and grammar are sufficient to mathematically formulate the bounded time high level specifications. A discrete path will be generated, that will meet the specifications with all timing constraints and, at the same time, it will optimize some cost function. A continuous trajectory satisfying the continuous dynamics of the robot will be generated from the discrete path using proper control laws.

Temporal Logic Verification of Stochastic Systems Using Barrier Certificates

“…x 2 (k + 1) = (1 − T )x 2 (k) − T x 2 (k)x 3 (k) + 0.025x 2 (k)w 2 (k), x 3 (k + 1) = (1 + bT )x 3 (k) + T x 1 (k)x 2 (k) + 0.025x 3 (k)w 3 (k), (16) where a = 10, b = 8/3, and T = 0.01. Noise terms w 1 (k), w 2 (k), and w 3 (k) are independent standard normal random variables.…”

“…This is achieved by relaxing supermartingale condition to c-martingale as also utilized in [27]. Correspondingly, instead of infinite-horizon specifications, we consider finite-horizon temporal specifications, which are more practical in the real life applications including motion planning problems [22,16,2]. In spirit, this work extends the idea of combining automata representation of the specification and barrier certificates, which is proposed in [33] for non-stochastic dynamics, in order to verify stochastic systems against specifications expressed as a fragment of LTL formulae, namely, safe LTL on finite traces.…”

Event-Triggered Controller Synthesis for Dynamical Systems with Temporal Logic Constraints

“…Thus, the dynamics constraint and logical constraint in (2) can jointly be represented by forming a product of the automata and the FTS. More detail on such construction and controller synthesis can be found in our earlier work [19]. To keep the paper short, we spare the details here, however, interested reader may see, for example, [20], [14].…”

“…From (19) one can verify that for all r > 0, w(r) > 0. Moreover using comparison lemma [21,Lemma 3.4], one can show for (19) that…”

Timed automata approach for motion planning using metric interval temporal logic

“…In this paper, we are interested in extending the idea of using LTL for time-unconstrained planning to use MITL for time-constrained motion planning. In [8], the authors proposed a method to represent time constrained planning task as an LTL formula rather than MITL formula. This formulation reduced the complexity of EXP-SPACE-complete for MITL to PSPACE-complete for LTL.…”