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 B\"uchi 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.
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This paper addresses the problem of copying an unknown assembly of primitives with known shape and appearance using information extracted from a single photograph by an off-the-shelf procedure for object detection and pose estimation. The proposed algorithm uses a simple combination of physical stability constraints, convex optimization and Monte Carlo tree search to plan assemblies as sequences of pick-and-place operations represented by STRIPS operators. It is efficient and, most importantly, robust to the errors in object detection and pose estimation unavoidable in any real robotic system. The proposed approach is demonstrated with thorough experiments on a UR5 manipulator.
Current challenges of the manufacturing industry require modular and changeable manufacturing systems that can be adapted to variable conditions with little effort. At the same time, production recipes typically represent important company know-how that should not be directly tied to changing plant configurations. Thus, there is a need to model general production recipes independent of specific plant layouts. For execution of such a recipe however, a binding to then available production resources needs to be made. In this contribution, select a suitable modeling language to model and execute such recipes. Furthermore, we present an approach to solve the issue of recipe modeling and execution in modular plants using semantically modeled capabilities and skills as well as BPMN. We make use of BPMN to model \emph{capability processes}, i.e. production processes referencing abstract descriptions of resource functions. These capability processes are not bound to a certain plant layout, as there can be multiple resources fulfilling the same capability. For execution, every capability in a capability process is replaced by a skill realizing it, effectively creating a \emph{skill process} consisting of various skill invocations. The presented solution is capable of orchestrating and executing complex processes that integrate production steps with typical IT functionalities such as error handling, user interactions and notifications. Benefits of the approach are demonstrated using a flexible manufacturing system.
Automated vehicles require the ability to cooperate with humans for smooth integration into today's traffic. While the concept of cooperation is well known, developing a robust and efficient cooperative trajectory planning method is still a challenge. One aspect of this challenge is the uncertainty surrounding the state of the environment due to limited sensor accuracy. This uncertainty can be represented by a Partially Observable Markov Decision Process. Our work addresses this problem by extending an existing cooperative trajectory planning approach based on Monte Carlo Tree Search for continuous action spaces. It does so by explicitly modeling uncertainties in the form of a root belief state, from which start states for trees are sampled. After the trees have been constructed with Monte Carlo Tree Search, their results are aggregated into return distributions using kernel regression. We apply two risk metrics for the final selection, namely a Lower Confidence Bound and a Conditional Value at Risk. It can be demonstrated that the integration of risk metrics in the final selection policy consistently outperforms a baseline in uncertain environments, generating considerably safer trajectories.
The hard thresholding technique plays a vital role in the development of algorithms for sparse signal recovery. By merging this technique and heavy-ball acceleration method which is a multi-step extension of the traditional gradient descent method, we propose the so-called heavy-ball-based hard thresholding (HBHT) and heavy-ball-based hard thresholding pursuit (HBHTP) algorithms for signal recovery. It turns out that the HBHT and HBHTP can successfully recover a $k$-sparse signal if the restricted isometry constant of the measurement matrix satisfies $\delta_{3k}<0.618 $ and $\delta_{3k}<0.577,$ respectively. The guaranteed success of HBHT and HBHTP is also shown under the conditions $\delta_{2k}<0.356$ and $\delta_{2k}<0.377,$ respectively. Moreover, the finite convergence and stability of the two algorithms are also established in this paper. Simulations on random problem instances are performed to compare the performance of the proposed algorithms and several existing ones. Empirical results indicate that the HBHTP performs very comparably to a few existing algorithms and it takes less average time to achieve the signal recovery than these existing methods.
Free-space-oriented roadmaps typically generate a series of convex geometric primitives, which constitute the safe region for motion planning. However, a static environment is assumed for this kind of roadmap. This assumption makes it unable to deal with dynamic obstacles and limits its applications. In this paper, we present a dynamic free-space roadmap, which provides feasible spaces and a navigation graph for safe quadrotor motion planning. Our roadmap is constructed by continuously seeding and extracting free regions in the environment. In order to adapt our map to environments with dynamic obstacles, we incrementally decompose the polyhedra intersecting with obstacles into obstacle-free regions, while the graph is also updated by our well-designed mechanism. Extensive simulations and real-world experiments demonstrate that our method is practically applicable and efficient.
Semantic place annotation can provide individual semantics, which can be of great help in the field of trajectory data mining. Most existing methods rely on annotated or external data and require retraining following a change of region, thus preventing their large-scale applications. Herein, we propose an unsupervised method denoted as UPAPP for the semantic place annotation of trajectories using spatiotemporal information. The Bayesian Criterion is specifically employed to decompose the spatiotemporal probability of the candidate place into spatial probability, duration probability, and visiting time probability. Spatial information in ROI and POI data is subsequently adopted to calculate the spatial probability. In terms of the temporal probabilities, the Term Frequency Inverse Document Frequency weighting algorithm is used to count the potential visits to different place types in the trajectories, and generates the prior probabilities of the visiting time and duration. The spatiotemporal probability of the candidate place is then combined with the importance of the place category to annotate the visited places. Validation with a trajectory dataset collected by 709 volunteers in Beijing showed that our method achieved an overall and average accuracy of 0.712 and 0.720, respectively, indicating that the visited places can be annotated accurately without any external data.
Consistent motion estimation is fundamental for all mobile autonomous systems. While this sounds like an easy task, often, it is not the case because of changing environmental conditions affecting odometry obtained from vision, Lidar, or the wheels themselves. Unsusceptible to challenging lighting and weather conditions, radar sensors are an obvious alternative. Usually, automotive radars return a sparse point cloud, representing the surroundings. Utilizing this information to motion estimation is challenging due to unstable and phantom measurements, which result in a high rate of outliers. We introduce a credible and robust probabilistic approach to estimate the ego-motion based on these challenging radar measurements; intended to be used within a loosely-coupled sensor fusion framework. Compared to existing solutions, evaluated on the popular nuScenes dataset and others, we show that our proposed algorithm is more credible while not depending on explicit correspondence calculation.
We describe a cognitive architecture intended to solve a wide range of problems based on the five identified principles of brain activity, with their implementation in three subsystems: logical-probabilistic inference, probabilistic formal concepts, and functional systems theory. Building an architecture involves the implementation of a task-driven approach that allows defining the target functions of applied applications as tasks formulated in terms of the operating environment corresponding to the task, expressed in the applied ontology. We provide a basic ontology for a number of practical applications as well as for the subject domain ontologies based upon it, describe the proposed architecture, and give possible examples of the execution of these applications in this architecture.
One of the most important problems in system identification and statistics is how to estimate the unknown parameters of a given model. Optimization methods and specialized procedures, such as Empirical Minimization (EM) can be used in case the likelihood function can be computed. For situations where one can only simulate from a parametric model, but the likelihood is difficult or impossible to evaluate, a technique known as the Two-Stage (TS) Approach can be applied to obtain reliable parametric estimates. Unfortunately, there is currently a lack of theoretical justification for TS. In this paper, we propose a statistical decision-theoretical derivation of TS, which leads to Bayesian and Minimax estimators. We also show how to apply the TS approach on models for independent and identically distributed samples, by computing quantiles of the data as a first step, and using a linear function as the second stage. The proposed method is illustrated via numerical simulations.
Binding operation is fundamental to many cognitive processes, such as cognitive map formation, relational reasoning, and language comprehension. In these processes, two different modalities, such as location and objects, events and their contextual cues, and words and their roles, need to be bound together, but little is known about the underlying neural mechanisms. Previous works introduced a binding model based on quadratic functions of bound pairs, followed by vector summation of multiple pairs. Based on this framework, we address following questions: Which classes of quadratic matrices are optimal for decoding relational structures? And what is the resultant accuracy? We introduce a new class of binding matrices based on a matrix representation of octonion algebra, an eight-dimensional extension of complex numbers. We show that these matrices enable a more accurate unbinding than previously known methods when a small number of pairs are present. Moreover, numerical optimization of a binding operator converges to this octonion binding. We also show that when there are a large number of bound pairs, however, a random quadratic binding performs as well as the octonion and previously-proposed binding methods. This study thus provides new insight into potential neural mechanisms of binding operations in the brain.
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