Incremental sampling-based algorithm for minimum-violation motion planning

Abstract

Abstract-This paper studies the problem of control strategy synthesis for dynamical systems with differential constraints to fulfill a given reachability goal while satisfying a set of safety rules. Particular attention is devoted to goals that become feasible only if a subset of the safety rules are violated. The proposed algorithm computes a control law, that minimizes the level of unsafety while the desired goal is guaranteed to be reached. This problem is motivated by an autonomous car navigating an urban environment while following rules of the road such as "always travel in right lane" and "do not change lanes frequently". Ideas behind sampling based motionplanning algorithms, such as Probabilistic Road Maps (PRMs) and Rapidly-exploring Random Trees (RRTs), are employed to incrementally construct a finite concretization of the dynamics as a durational Kripke structure. In conjunction with this, a weighted finite automaton that captures the safety rules is used in order to find an optimal trajectory that minimizes the violation of safety rules. We prove that the proposed algorithm guarantees asymptotic optimality, i.e., almost-sure convergence to optimal solutions. We present results of simulation experiments and an implementation on an autonomous urban mobility-on-demand system.

From Specifications to Behavior: Maneuver Verification in a Semantic State Space

“…Reyes Castro et al [17] translate LTL specifications into an automaton. A second automaton is created as a discrete abstraction of an RRT*-explored workspace.…”

Minimum Constraint Displacement Motion Planning

“…The minimum constraint removal [7] problem asks to remove the fewest constraints in order to yield a feasible path. Similar work has addressed violating lowpriority tasks for multi-objective tasks specified in terms of LTL formulas [3]. Rather than removing constraints in binary fashion, MCD considers continuous changes.…”

Reactive sampling-based path planning with temporal logic specifications

“…Karaman and Frazzoli (2011) proposed RRT * and PRM * , the probabilistically optimal counterparts of RRT and PRM. Sampling-based methods have been employed in dealing with kinematic constraints (Hauser and Zhou, 2016; Kleinbort et al, 2019; Moore et al, 2014; Webb and van den Berg, 2013), stochastic robot models (Agha-mohammadi et al, 2014; Burns and Brock, 2007; Hauser, 2011; van den Berg et al, 2011; Vasile et al, 2016), multi-robot systems (Dobson et al, 2017; Kantaros and Zavlanos, 2019), in applications such as autonomous driving (Kuwata et al, 2009; Reyes Castro et al, 2013; Vasile et al, 2017b), manipulation (He et al, 2017; Muhayyuddin et al, 2018), and surgery (Baykal et al, 2019). A more detailed exposition of sampling-based methods can be found in Kingston et al (2018).…”

“…To deal with the state-space explosion problem, they propose a layered path planning approach that uses a cell decomposition of the configuration space for high-level temporal planning and expansive space trees (EST) for kino-dynamic planning of the low-level, cell-to-cell motion. The on-line algorithm from Tumova et al (2013) and Reyes Castro et al (2013) finds minimum violating paths for a robot when the global specification cannot be enforced completely. In Livingston and Murray (2013) and Livingston et al (2013), the global specifications are given in the GR(1) fragment of LTL, and on-line local re-planning is done through patching invalidated paths based on μ -calculus specifications.…”