arXiv subjects

Zhen Kan

Publications and source records attributed to Zhen Kan.

27 records · Page 2Linked to original sources

arXiv2022

Modular Deep Reinforcement Learning for Continuous Motion Planning with Temporal Logic

This paper investigates the motion planning of autonomous dynamical systems modeled by Markov decision processes (MDP) with unknown transition probabilities over continuous state and action spaces. Linear temporal logic (LTL) is used to specify high-level tasks over infinite horizon, which can be converted into a limit deterministic generalized Büchi automaton (LDGBA) with several accepting sets. The novelty is to design an embedded product MDP (EP-MDP) between the LDGBA and the MDP by incorporating a synchronous tracking-frontier function to record unvisited accepting sets of the automaton, and to facilitate the satisfaction of the accepting conditions. The proposed LDGBA-based reward shaping and discounting schemes for the model-free reinforcement learning (RL) only depend on the EP-MDP states and can overcome the issues of sparse rewards. Rigorous analysis shows that any RL method that optimizes the expected discounted return is guaranteed to find an optimal policy whose traces maximize the satisfaction probability. A modular deep deterministic policy gradient (DDPG) is then developed to generate such policies over continuous state and action spaces. The performance of our framework is evaluated via an array of OpenAI gym environments.

cs.LG↗

arXiv2021

Optimal Probabilistic Motion Planning with Potential Infeasible LTL Constraints

This paper studies optimal motion planning subject to motion and environment uncertainties. By modeling the system as a probabilistic labeled Markov decision process (PL-MDP), the control objective is to synthesize a finite-memory policy, under which the agent satisfies complex high-level tasks expressed as linear temporal logic (LTL) with desired satisfaction probability. In particular, the cost optimization of the trajectory that satisfies infinite horizon tasks is considered, and the trade-off between reducing the expected mean cost and maximizing the probability of task satisfaction is analyzed. Instead of using traditional Rabin automata, the LTL formulas are converted to limit-deterministic Büchi automata (LDBA) with a reachability acceptance condition and a compact graph structure. The novelty of this work lies in considering the cases where LTL specifications can be potentially infeasible and developing a relaxed product MDP between PL-MDP and LDBA. The relaxed product MDP allows the agent to revise its motion plan whenever the task is not fully feasible and quantify the revised plan's violation measurement. A multi-objective optimization problem is then formulated to jointly consider the probability of task satisfaction, the violation with respect to original task constraints, and the implementation cost of the policy execution. The formulated problem can be solved via coupled linear programs. To the best of our knowledge, this work first bridges the gap between probabilistic planning revision of potential infeasible LTL specifications and optimal control synthesis of both plan prefix and plan suffix of the trajectory over the infinite horizons. Experimental results are provided to demonstrate the effectiveness of the proposed framework.

cs.RO↗

arXiv2021

Online Motion Planning with Soft Metric Interval Temporal Logic in Unknown Dynamic Environment

Motion planning of an autonomous system with high-level specifications has wide applications. However, research of formal languages involving timed temporal logic is still under investigation. Furthermore, many existing results rely on a key assumption that user-specified tasks are feasible in the given environment. Challenges arise when the operating environment is dynamic and unknown since the environment can be found prohibitive, leading to potentially conflicting tasks where pre-specified timed missions cannot be fully satisfied. Such issues become even more challenging when considering time-bound requirements. To address these challenges, this work proposes a control framework that considers hard constraints to enforce safety requirements and soft constraints to enable task relaxation. The metric interval temporal logic (MITL) specifications are employed to deal with time-bound constraints. By constructing a relaxed timed product automaton, an online motion planning strategy is synthesized with a receding horizon controller to generate policies, achieving multiple objectives in decreasing order of priority 1) formally guarantee the satisfaction of hard safety constraints; 2) mostly fulfill soft timed tasks; and 3) collect time-varying rewards as much as possible. Another novelty of the relaxed structure is to consider violations of both time and tasks for infeasible cases. Simulation results are provided to validate the proposed approach.

cs.RO↗

arXiv2021

Receding Horizon Control Based Online Motion Planning with Partially Infeasible LTL Specifications

This work considers online optimal motion planning of an autonomous agent subject to linear temporal logic (LTL) constraints. The environment is dynamic in the sense of containing mobile obstacles and time-varying areas of interest (i.e., time-varying reward and workspace properties) to be visited by the agent. Since user-specified tasks may not be fully realized (i.e., partially infeasible), this work considers hard and soft LTL constraints, where hard constraints enforce safety requirement (e.g. avoid obstacles) while soft constraints represent tasks that can be relaxed to not strictly follow user specifications. The motion planning of the agent is to generate policies, in decreasing order of priority, to 1) formally guarantee the satisfaction of safety constraints; 2) mostly satisfy soft constraints (i.e., minimize the violation cost if desired tasks are partially infeasible); and 3) optimize the objective of rewards collection (i.e., visiting dynamic areas of more interests). To achieve these objectives, a relaxed product automaton, which allows the agent to not strictly follow the desired LTL constraints, is constructed. A utility function is developed to quantify the differences between the revised and the desired motion plan, and the accumulated rewards are designed to bias the motion plan towards those areas of more interests. Receding horizon control is synthesized with an LTL formula to maximize the accumulated utilities over a finite horizon, while ensuring that safety constraints are fully satisfied and soft constraints are mostly satisfied. Simulation and experiment results are provided to demonstrate the effectiveness of the developed motion strategy.

cs.RO↗

arXiv2021

Reinforcement Learning Based Temporal Logic Control with Maximum Probabilistic Satisfaction

This paper presents a model-free reinforcement learning (RL) algorithm to synthesize a control policy that maximizes the satisfaction probability of linear temporal logic (LTL) specifications. Due to the consideration of environment and motion uncertainties, we model the robot motion as a probabilistic labeled Markov decision process with unknown transition probabilities and unknown probabilistic label functions. The LTL task specification is converted to a limit deterministic generalized Büchi automaton (LDGBA) with several accepting sets to maintain dense rewards during learning. The novelty of applying LDGBA is to construct an embedded LDGBA (E-LDGBA) by designing a synchronous tracking-frontier function, which enables the record of non-visited accepting sets without increasing dimensional and computational complexity. With appropriate dependent reward and discount functions, rigorous analysis shows that any method that optimizes the expected discount return of the RL-based approach is guaranteed to find the optimal policy that maximizes the satisfaction probability of the LTL specifications. A model-free RL-based motion planning strategy is developed to generate the optimal policy in this paper. The effectiveness of the RL-based control synthesis is demonstrated via simulation and experimental results.

cs.FL↗

arXiv2014

Decentralized Rendezvous of Nonholonomic Robots with Sensing and Connectivity Constraints

A group of wheeled robots with nonholonomic constraints is considered to rendezvous at a common specified setpoint with a desired orientation while maintaining network connectivity and ensuring collision avoidance within the robots. Given communication and sensing constraints for each robot, only a subset of the robots are aware or informed of the global destination, and the remaining robots must move within the network connectivity constraint so that the informed robots can guide the group to the goal. The mobile robots are also required to avoid collisions with each other outside a neighborhood of the common rendezvous point. To achieve the rendezvous control objective, decentralized time-varying controllers are developed based on a navigation function framework to steer the robots to perform rendezvous while preserving network connectivity and ensuring collision avoidance. Only local sensing feedback, which includes position feedback from immediate neighbors and absolute orientation measurement, is used to navigate the robots and enables radio silence during navigation. Simulation results demonstrate the performance of the developed approach.

eess.SY↗

arXiv2014

Containment Control for a Social Network with State-Dependent Connectivity

Social interactions influence our thoughts, opinions and actions. In this paper, social interactions are studied within a group of individuals composed of influential social leaders and followers. Each person is assumed to maintain a social state, which can be an emotional state or an opinion. Followers update their social states based on the states of local neighbors, while social leaders maintain a constant desired state. Social interactions are modeled as a general directed graph where each directed edge represents an influence from one person to another. Motivated by the non-local property of fractional-order systems, the social response of individuals in the network are modeled by fractional-order dynamics whose states depend on influences from local neighbors and past experiences. A decentralized influence method is then developed to maintain existing social influence between individuals (i.e., without isolating peers in the group) and to influence the social group to a common desired state (i.e., within a convex hull spanned by social leaders). Mittag-Leffler stability methods are used to prove asymptotic stability of the networked fractional-order system.

eess.SY↗

arXiv2014

Navigation Function Based Decentralized Control of A Multi-Agent System with Network Connectivity Constraints

A wide range of applications require or can benefit from collaborative behavior of a group of agents. The technical challenge addressed in this chapter is the development of a decentralized control strategy that enables each agent to independently navigate to ensure agents achieve a collective goal while maintaining network connectivity. Specifically, cooperative controllers are developed for networked agents with limited sensing and network connectivity constraints. By modeling the interaction among the agents as a graph, several different approaches to address the problems of preserving network connectivity are presented, with the focus on a method that utilizes navigation function frameworks. By modeling network connectivity constraints as artificial obstacles in navigation functions, a decentralized control strategy is presented in two particular applications, formation control and rendezvous for a system of autonomous agents, which ensures global convergence to the unique minimum of the potential field (i.e., desired formation or desired destination) while preserving network connectivity. Simulation results are provided to demonstrate the developed strategy.

eess.SY↗

arXiv2013

Decentralized formation control with connectivity maintenance and collision avoidance under limited and intermittent sensing

A decentralized switched controller is developed for dynamic agents to perform global formation configuration convergence while maintaining network connectivity and avoiding collision within agents and between stationary obstacles, using only local feedback under limited and intermittent sensing. Due to the intermittent sensing, constant position feedback may not be available for agents all the time. Intermittent sensing can also lead to a disconnected network or collisions between agents. Using a navigation function framework, a decentralized switched controller is developed to navigate the agents to the desired positions while ensuring network maintenance and collision avoidance.

eess.SY↗