Classical reactive synthesis approaches aim to synthesize a reactive system that always satisfies a given specification. These approaches often reduce to playing a two-player zero-sum game where the goal is to synthesize a winning strategy. However, in many pragmatic domains, such as robotics, a winning strategy does not always exist, yet it is desirable for the system to make an effort to satisfy its requirements instead of "giving up." To this end, this paper investigates the notion of admissible strategies, which formalize "doing-your-best", in quantitative reachability games. We show that, unlike the qualitative case, memoryless strategies are not sufficient to capture all admissible strategies, making synthesis a challenging task. In addition, we prove that admissible strategies always exist but may produce undesirable optimistic behaviors. To mitigate this, we propose admissible winning strategies, which enforce the best possible outcome while being admissible. We show that both strategies always exist but are not memoryless. We provide necessary and sufficient conditions for the existence of both strategies and propose synthesis algorithms. Finally, we illustrate the strategies on gridworld and robot manipulator domains.

In this paper, we present a controller framework that synthesizes control policies for Jump Markov Linear Systems subject to stochastic mode switches and imperfect mode estimation. Our approach builds on safe and robust methods for Model Predictive Control (MPC), but in contrast to existing approaches that either optimize without regard to feasibility or utilize soft constraints that increase computational requirements, we employ a safe and robust control approach informed by the feasibility of the optimization problem. We formulate and encode finite horizon safety for multiple model systems in our MPC design using Control Barrier Functions (CBFs). When subject to inaccurate hybrid state estimation, our feasibility-guided MPC generates a control policy that is maximally robust to uncertainty in the system’s modes. We evaluate our approach on an orbital rendezvous problem and a six degree-of-freedom hexacopter under several scenarios and benchmarks to demonstrate the utility of the framework. Results indicate that the proposed technique of maximizing the robustness horizon, and the use of CBFs for safety awareness, improve the overall safety and performance of MPC for Jump Markov Linear Systems.

Many sequential decision problems involve optimizing one objective function while imposing constraints on other objectives. Constrained Partially Observable Markov Decision Processes (C-POMDP) model this case with transition uncertainty and partial observability. In this work, we first show that C-POMDPs violate the optimal substructure property over successive decision steps and thus may exhibit behaviors that are undesirable for some (e.g., safety critical) applications. Additionally, online re-planning in C-POMDPs is often ineffective due to the inconsistency resulting from this violation. To address these drawbacks, we introduce the Recursively-Constrained POMDP (RC-POMDP), which 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 for RC-POMDPs. Evaluations on benchmark problems demonstrate the efficacy of our algorithm and show that policies for RC-POMDPs produce more desirable behaviors than policies for C-POMDPs.

Partially Observable Markov Decision Processes (POMDPs) are powerful models for sequential decision making under transition and observation uncertainties. This paper studies the challenging yet important problem in POMDPs known as the (indefinite-horizon) Maximal Reachability Probability Problem (MRPP), where the goal is to maximize the probability of reaching some target states. This is also a core problem in model checking with logical specifications and is naturally undiscounted (discount factor is one). Inspired by the success of point-based methods developed for discounted problems, we study their extensions to MRPP. Specifically, we focus on trial-based heuristic search value iteration techniques and present a novel algorithm that leverages the strengths of these techniques for efficient exploration of the belief space (informed search via value bounds) while addressing their drawbacks in handling loops for indefinite-horizon problems. The algorithm produces policies with two-sided bounds on optimal reachability probabilities. We prove convergence to an optimal policy from below under certain conditions. Experimental evaluations on a suite of benchmarks show that our algorithm outperforms existing methods in almost all cases in both probability guarantees and computation time.

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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.

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 of the motion planner with respect to the measure, and demonstrate the effectiveness of our approach on several case studies.

We consider the problem of motion and communication planning under uncertainty with 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 and demonstrate computational efficiency and asymptotic optimality of the planner.

In this paper, we address the problem of sampling-based motion planning under motion and measurement un-certainty with probabilistic guarantees. We generalize traditional sampling-based, tree-based motion planning algorithms for deterministic systems and propose belief-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.

This paper addresses the safe path planning problem for autonomous mobility with multi-modal perception uncertainties. Specifically, we assume that different sensor inputs lead to different Gaussian process regulated perception uncertainties (named as multi-modal perception uncertainties). We implement a Bayesian inference algorithm, which merges the multi-modal GP-regulated uncertainties into a unified one and translates the unified uncertainty into a dynamic risk map. With the safe path planner taking the risk map as input, we are able to plan a safe path for the autonomous vehicle to follow. Experimental results on an autonomous golf cart testbed validate the applicability and efficiency of the proposed algorithm.

Autonomous urban driving among human-driven cars requires a holistic understanding of road rules, driver intents and driving styles. This is challenging as a short-term, single instance, driver intent of lane change may not correspond to their driving styles for a longer duration. This paper presents an interactive behavior planner which accounts for road context, short-term driver intent, and long-term driving style to infer beliefs over the latent states of surrounding vehicles. We use a specialized Partially Observable Markov Decision Process to provide risk-averse decisions. Specifically, we consider adversarial driving scenarios caused by irrational drivers to validate the robustness of our proposed interactive behavior planner in simulation as well as on a full-size self-driving car. Our experimental results show that our algorithm enables safer and more travel time-efficient autonomous driving compared to baselines even in adversarial scenarios.

We present a novel autonomous driving system which uses the road contextual information and intentions of other road users for urban driving. Unlike highways, urban environments require the drivers to follow traffic signs and signals while using their best judgment for anomalous situations. In such scenarios, a self-driving car needs to understand and take into account the uncertainties in the environment to plan and decide its action accordingly. Our planner models the intentions of the surrounding vehicles leveraging a neural network, and integrates the road contextual information to reduce its environment uncertainties and also speed up the decision making process. We validate our planner in simulation and in a real urban environment. Our experimental results show that integrating intention inference and road contextual information for prediction, planning and decision making help improve safety and efficiency of our autonomous driving system.