Recursively-Constrained Partially Observable Markov Decision Processes

In many problems, it is desirable to optimize an objective function while imposing constraints on some other aspect of the problem. A Constrained Partially Observable Markov Decision Process (C-POMDP) allows modelling of such problems while subject to transition uncertainty and partial observability. Typically, the constraints in C-POMDPs enforce a threshold on expected cumulative costs starting from an initial state distribution. In this work, we first show that optimal C-POMDP policies may violate Bellman's principle of optimality and thus may exhibit pathological behaviors, which can be undesirable for many applications. To address this drawback, we introduce a new formulation, the Recursively-Constrained POMDP (RC-POMDP), that imposes additional history dependent cost constraints on the C-POMDP. We show that, unlike C-POMDPs, RC-POMDPs always have deterministic optimal policies, and that optimal policies obey Bellman's principle of optimality. We also present a point-based dynamic programming algorithm that synthesizes optimal policies for RC-POMDPs. In our evaluations, we show that policies for RC-POMDPs produce more desirable behavior than policies for C-POMDPs and demonstrate the efficacy of our algorithm across a set of benchmark problems.

Sampling-based Reactive Synthesis for Nondeterministic Hybrid Systems

This paper introduces a sampling-based strategy synthesis algorithm for nondeterministic hybrid systems with complex continuous dynamics under temporal and reachability constraints. We view the evolution of the hybrid system as a two-player game, where the nondeterminism is an adversarial player whose objective is to prevent achieving temporal and reachability goals. The aim is to synthesize a winning strategy -- a reactive (robust) strategy that guarantees the satisfaction of the goals under all possible moves of the adversarial player. The approach is based on growing a (search) game-tree in the hybrid space by combining a sampling-based planning method with a novel bandit-based technique to select and improve on partial strategies. We provide conditions under which the algorithm is probabilistically complete, i.e., if a winning strategy exists, the algorithm will almost surely find it. The case studies and benchmark results show that the algorithm is general and consistently outperforms the state of the art.

Planning with SiMBA: Motion Planning under Uncertainty for Temporal Goals using Simplified Belief Guides

This paper presents a new multi-layered algorithm for motion planning under motion and sensing uncertainties for Linear Temporal Logic specifications. We propose a technique to guide a sampling-based search tree in the combined task and belief space using trajectories from a simplified model of the system, to make the problem computationally tractable. Our method eliminates the need to construct fine and accurate finite abstractions. We prove correctness and probabilistic completeness of our algorithm, and illustrate the benefits of our approach on several case studies. Our results show that guidance with a simplified belief space model allows for significant speed-up in planning for complex specifications.

Chance-Constrained Motion Planning with Event-Triggered Estimation

We consider the problem of autonomous navigation using limited information from a remote sensor network. Because the remote sensors are power and bandwidth limited, we use event-triggered (ET) estimation to manage communication costs. We introduce a fast and efficient sampling-based planner which computes motion plans coupled with ET communication strategies that minimize communication costs, while satisfying constraints on the probability of reaching the goal region and the point-wise probability of collision. We derive a novel method for offline propagation of the expected state distribution, and corresponding bounds on this distribution. These bounds are used to evaluate the chance constraints in the algorithm. Case studies establish the validity of our approach, demonstrating fast computation of optimal plans.

Stochastic Robustness Interval for Motion Planning with Signal Temporal Logic

In this work, we present a novel robustness measure for continuous-time stochastic trajectories with respect to Signal Temporal Logic (STL) specifications. We show the soundness of the measure and develop a monitor for reasoning about partial trajectories. Using this monitor, we introduce an STL sampling-based motion planning algorithm for robots under uncertainty. Given a minimum robustness requirement, this algorithm finds satisfying motion plans; alternatively, the algorithm also optimizes for the measure. We prove probabilistic completeness and asymptotic optimality, and demonstrate the effectiveness of our approach on several case studies.

Automaton-Guided Control Synthesis for Signal Temporal Logic Specifications

This paper presents an algorithmic framework for control synthesis of continuous dynamical systems subject to signal temporal logic (STL) specifications. We propose a novel algorithm to obtain a time-partitioned finite automaton from an STL specification, and introduce a multi-layered framework that utilizes this automaton to guide a sampling-based search tree both spatially and temporally. Our approach is able to synthesize a controller for nonlinear dynamics and polynomial predicate functions. We prove the correctness and probabilistic completeness of our algorithm, and illustrate the efficiency and efficacy of our framework on several case studies. Our results show an order of magnitude speedup over the state of the art.

Gaussian Belief Trees for Chance Constrained Asymptotically Optimal Motion Planning

In this paper, we address the problem of sampling-based motion planning under motion and measurement uncertainty with probabilistic guarantees. We generalize traditional sampling-based tree-based motion planning algorithms for deterministic systems and propose belief-$\mathcal{A}$, a framework that extends any kinodynamical tree-based planner to the belief space for linear (or linearizable) systems. We introduce appropriate sampling techniques and distance metrics for the belief space that preserve the probabilistic completeness and asymptotic optimality properties of the underlying planner. We demonstrate the efficacy of our approach for finding safe low-cost paths efficiently and asymptotically optimally in simulation, for both holonomic and non-holonomic systems.

Online Multi-Target Tracking for Maneuvering Vehicles in Dynamic Road Context

Target detection and tracking provides crucial information for motion planning and decision making in autonomous driving. This paper proposes an online multi-object tracking (MOT) framework with tracking-by-detection for maneuvering vehicles under motion uncertainty in dynamic road context. We employ a point cloud based vehicle detector to provide real-time 3D bounding boxes of detected vehicles and conduct the online bipartite optimization of the maneuver-orientated data association between the detections and the targets. Kalman Filter (KF) is adopted as the backbone for multi-object tracking. In order to entertain the maneuvering uncertainty, we leverage the interacting multiple model (IMM) approach to obtain the \textit{a-posterior} residual as the cost for each association hypothesis, which is calculated with the hybrid model posterior (after mode-switch). Road context is integrated to conduct adjustments of the time varying transition probability matrix (TPM) of the IMM to regulate the maneuvers according to road segments and traffic sign/signals, with which the data association is performed in a unified spatial-temporal fashion. Experiments show our framework is able to effectively track multiple vehicles with maneuvers subject to dynamic road context and localization drift.