93 research outputs found
Sampling-Based Temporal Logic Path Planning
In this paper, we propose a sampling-based motion planning algorithm that
finds an infinite path satisfying a Linear Temporal Logic (LTL) formula over a
set of properties satisfied by some regions in a given environment. The
algorithm has three main features. First, it is incremental, in the sense that
the procedure for finding a satisfying path at each iteration scales only with
the number of new samples generated at that iteration. Second, the underlying
graph is sparse, which guarantees the low complexity of the overall method.
Third, it is probabilistically complete. Examples illustrating the usefulness
and the performance of the method are included.Comment: 8 pages, 4 figures; extended version of the paper presented at IROS
201
Motion planning and control: a formal methods approach
Control of complex systems satisfying rich temporal specification has become an increasingly important research area in fields such as robotics, control, automotive, and manufacturing. Popular specification languages include temporal logics, such as Linear Temporal Logic (LTL) and Computational Tree Logic (CTL), which extend propositional logic to capture the temporal sequencing of system properties. The focus of this dissertation is on the control of high-dimensional systems and on timed specifications that impose explicit time bounds on the satisfaction of tasks. This work proposes and evaluates methods and algorithms for synthesizing provably correct control policies that deal with the scalability problems. Ideas and tools from formal verification, graph theory, and incremental computing are used to synthesize satisfying control strategies. Finite abstractions of the systems are generated, and then composed with automata encoding the specifications.
The first part of this dissertation introduces a sampling-based motion planning algorithm that combines long-term temporal logic goals with short-term reactive requirements. The specification has two parts: (1) a global specification given as an LTL formula over a set of static service requests that occur at the regions of a known environment, and (2) a local specification that requires servicing a set of dynamic requests that can be sensed locally during the execution. The proposed computational framework consists of two main ingredients: (a) an off-line sampling-based algorithm for the construction of a global transition system that contains a path satisfying the LTL formula, and (b) an on-line sampling-based algorithm to generate paths that service the local requests, while making sure that the satisfaction of the global specification is not affected.
The second part of the dissertation focuses on stochastic systems with temporal and uncertainty constraints. A specification language called Gaussian Distribution Temporal Logic is introduced as an extension of Boolean logic that incorporates temporal evolution and noise mitigation directly into the task specifications. A sampling-based algorithm to synthesize control policies is presented that generates a transition system in the belief space and uses local feedback controllers to break the curse of history associated with belief space planning. Switching control policies are then computed using a product Markov Decision Process between the transition system and the Rabin automaton encoding the specification.The approach is evaluated in experiments using a camera network and ground robot.
The third part of this dissertation focuses on control of multi-vehicle systems with timed specifications and charging constraints. A rich expressivity language called Time Window Temporal Logic (TWTL) that describes time bounded specifications is introduced. The temporal relaxation of TWTL formulae with respect to the deadlines of tasks is also discussed. The key ingredient of the solution is an algorithm to translate a TWTL formula to an annotated finite state automaton that encodes all possible temporal relaxations of the given formula. The annotated automata are composed with transition systems encoding the motion of all vehicles, and with charging models to produce control strategies for all vehicles such that the overall system satisfies the mission specification. The methods are evaluated in simulation and experimental trials with quadrotors and charging stations
Reinforcement Learning With Temporal Logic Rewards
Reinforcement learning (RL) depends critically on the choice of reward
functions used to capture the de- sired behavior and constraints of a robot.
Usually, these are handcrafted by a expert designer and represent heuristics
for relatively simple tasks. Real world applications typically involve more
complex tasks with rich temporal and logical structure. In this paper we take
advantage of the expressive power of temporal logic (TL) to specify complex
rules the robot should follow, and incorporate domain knowledge into learning.
We propose Truncated Linear Temporal Logic (TLTL) as specifications language,
that is arguably well suited for the robotics applications, together with
quantitative semantics, i.e., robustness degree. We propose a RL approach to
learn tasks expressed as TLTL formulae that uses their associated robustness
degree as reward functions, instead of the manually crafted heuristics trying
to capture the same specifications. We show in simulated trials that learning
is faster and policies obtained using the proposed approach outperform the ones
learned using heuristic rewards in terms of the robustness degree, i.e., how
well the tasks are satisfied. Furthermore, we demonstrate the proposed RL
approach in a toast-placing task learned by a Baxter robot
Time Window Temporal Logic
This paper introduces time window temporal logic (TWTL), a rich expressivity
language for describing various time bounded specifications. In particular, the
syntax and semantics of TWTL enable the compact representation of serial tasks,
which are typically seen in robotics and control applications. This paper also
discusses the relaxation of TWTL formulae with respect to deadlines of tasks.
Efficient automata-based frameworks to solve synthesis, verification and
learning problems are also presented. The key ingredient to the presented
solution is an algorithm to translate a TWTL formula to an annotated finite
state automaton that encodes all possible temporal relaxations of the
specification. Case studies illustrating the expressivity of the logic and the
proposed algorithms are included
Time window temporal logic
This paper introduces time window temporal logic (TWTL), a rich expressive language for describing various time bounded specifications. In particular, the syntax and semantics of TWTL enable the compact representation of serial tasks, which are prevalent in various applications including robotics, sensor systems, and manufacturing systems. This paper also discusses the relaxation of TWTL formulae with respect to the deadlines of the tasks. Efficient automata-based frameworks are presented to solve synthesis, verification and learning problems. The key ingredient to the presented solution is an algorithm to translate a TWTL formula to an annotated finite state automaton that encodes all possible temporal relaxations of the given formula. Some case studies are presented to illustrate the expressivity of the logic and the proposed algorithms
Safety-Critical Learning of Robot Control with Temporal Logic Specifications
Reinforcement learning (RL) is a promising approach. However, success is
limited to real-world applications, because ensuring safe exploration and
facilitating adequate exploitation is a challenge for controlling robotic
systems with unknown models and measurement uncertainties. The learning problem
becomes even more difficult for complex tasks over continuous state-action. In
this paper, we propose a learning-based robotic control framework consisting of
several aspects: (1) we leverage Linear Temporal Logic (LTL) to express complex
tasks over infinite horizons that are translated to a novel automaton
structure; (2) we detail an innovative reward scheme for LTL satisfaction with
a probabilistic guarantee. Then, by applying a reward shaping technique, we
develop a modular policy-gradient architecture exploiting the benefits of the
automaton structure to decompose overall tasks and enhance the performance of
learned controllers; (3) by incorporating Gaussian Processes (GPs) to estimate
the uncertain dynamic systems, we synthesize a model-based safe exploration
during the learning process using Exponential Control Barrier Functions (ECBFs)
that generalize systems with high-order relative degrees; (4) to further
improve the efficiency of exploration, we utilize the properties of LTL
automata and ECBFs to propose a safe guiding process. Finally, we demonstrate
the effectiveness of the framework via several robotic environments. We show an
ECBF-based modular deep RL algorithm that achieves near-perfect success rates
and safety guarding with high probability confidence during training.Comment: Under Review. arXiv admin note: text overlap with arXiv:2102.1285
Improving the Universality Results of Enzymatic Numerical P Systems
This paper provides the proof that Enzymatic Numerical P Sytems with
deterministic, but parallel, execution model are universal, even when the production
functions used are polynomials of degree 1. This extends previous known results and
provides the optimal case in terms of polynomial degree
Energy-Constrained Active Exploration Under Incremental-Resolution Symbolic Perception
In this work, we consider the problem of autonomous exploration in search of
targets while respecting a fixed energy budget. The robot is equipped with an
incremental-resolution symbolic perception module wherein the perception of
targets in the environment improves as the robot's distance from targets
decreases. We assume no prior information about the total number of targets,
their locations as well as their possible distribution within the environment.
This work proposes a novel decision-making framework for the resulting
constrained sequential decision-making problem by first converting it into a
reward maximization problem on a product graph computed offline. It is then
solved online as a Mixed-Integer Linear Program (MILP) where the knowledge
about the environment is updated at each step, combining automata-based and
MILP-based techniques. We demonstrate the efficacy of our approach with the
help of a case study and present empirical evaluation in terms of expected
regret. Furthermore, the runtime performance shows that online planning can be
efficiently performed for moderately-sized grid environments
Control Barrier Function for Linearizable Systems with High Relative Degrees from Signal Temporal Logics: A Reference Governor Approach
This paper considers the safety-critical navigation problem with Signal
Temporal Logic (STL) tasks. We developed an explicit reference governor-guided
control barrier function (ERG-guided CBF) method that enables the application
of first-order CBFs to high-order linearizable systems. This method
significantly reduces the conservativeness of the existing CBF approaches for
high-order systems. Furthermore, our framework provides safety-critical
guarantees in the sense of obstacle avoidance by constructing the margin of
safety and updating direction of safe evolution in the agent's state space. To
improve control performance and enhance STL satisfaction, we employ efficient
gradient-based methods for iteratively learning optimal parameters of
ERG-guided CBF. We validate the algorithm through both high-order linear and
nonlinear systems. A video demonstration can be found on:
\url{https://youtu.be/ZRmsA2FeFR4
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