A Survey on Passing-through Control of Multi-Robot Systems in Cluttered Environments

This survey presents a comprehensive review of various methods and algorithms related to passing-through control of multi-robot systems in cluttered environments. Numerous studies have investigated this area, and we identify several avenues for enhancing existing methods. This survey describes some models of robots and commonly considered control objectives, followed by an in-depth analysis of four types of algorithms that can be employed for passing-through control: leader-follower formation control, multi-robot trajectory planning, control-based methods, and virtual tube planning and control. Furthermore, we conduct a comparative analysis of these techniques and provide some subjective and general evaluations.Comment: 18 pages, 19 figure

Certified Reinforcement Learning with Logic Guidance

This paper proposes the first model-free Reinforcement Learning (RL) framework to synthesise policies for unknown, and continuous-state Markov Decision Processes (MDPs), such that a given linear temporal property is satisfied. We convert the given property into a Limit Deterministic Buchi Automaton (LDBA), namely a finite-state machine expressing the property. Exploiting the structure of the LDBA, we shape a synchronous reward function on-the-fly, so that an RL algorithm can synthesise a policy resulting in traces that probabilistically satisfy the linear temporal property. This probability (certificate) is also calculated in parallel with policy learning when the state space of the MDP is finite: as such, the RL algorithm produces a policy that is certified with respect to the property. Under the assumption of finite state space, theoretical guarantees are provided on the convergence of the RL algorithm to an optimal policy, maximising the above probability. We also show that our method produces ''best available'' control policies when the logical property cannot be satisfied. In the general case of a continuous state space, we propose a neural network architecture for RL and we empirically show that the algorithm finds satisfying policies, if there exist such policies. The performance of the proposed framework is evaluated via a set of numerical examples and benchmarks, where we observe an improvement of one order of magnitude in the number of iterations required for the policy synthesis, compared to existing approaches whenever available.Comment: This article draws from arXiv:1801.08099, arXiv:1809.0782

Efficient Second-Order Shape-Constrained Function Fitting

We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including monotonicity, Lipschitz-continuity and convexity, and more generally, any shape constraint expressible by bounds on first- and/or second-order differences. Our algorithm computes an approximation with additive error $\varepsilon$ in $O\left(n \log \frac{U}{\varepsilon} \right)$ time, where $U$ captures the range of input values. We also give a simple greedy algorithm that runs in $O(n)$ time for the special case of unweighted $L_{\infty}$ convex regression. These are the first (near-)linear-time algorithms for second-order-constrained function fitting. To achieve these results, we use a novel geometric interpretation of the underlying dynamic programming problem. We further show that a generalization of the corresponding problems to directed acyclic graphs (DAGs) is as difficult as linear programming.Comment: accepted for WADS 2019; (v2 fixes various typos

Efficient Second-Order Shape-Constrained Function Fitting

We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including monotonicity, Lipschitz-continuity and convexity, and more generally, any shape constraint expressible by bounds on first- and/or second-order differences. Our algorithm computes an approximation with additive error $\varepsilon$ in $O\left(n \log \frac{U}{\varepsilon} \right)$ time, where $U$ captures the range of input values. We also give a simple greedy algorithm that runs in $O(n)$ time for the special case of unweighted $L_{\infty}$ convex regression. These are the first (near-)linear-time algorithms for second-order-constrained function fitting. To achieve these results, we use a novel geometric interpretation of the underlying dynamic programming problem. We further show that a generalization of the corresponding problems to directed acyclic graphs (DAGs) is as difficult as linear programming

Spatial land-use inventory, modeling, and projection/Denver metropolitan area, with inputs from existing maps, airphotos, and LANDSAT imagery

A landscape model was constructed with 34 land-use, physiographic, socioeconomic, and transportation maps. A simple Markov land-use trend model was constructed from observed rates of change and nonchange from photointerpreted 1963 and 1970 airphotos. Seven multivariate land-use projection models predicting 1970 spatial land-use changes achieved accuracies from 42 to 57 percent. A final modeling strategy was designed, which combines both Markov trend and multivariate spatial projection processes. Landsat-1 image preprocessing included geometric rectification/resampling, spectral-band, and band/insolation ratioing operations. A new, systematic grid-sampled point training-set approach proved to be useful when tested on the four orginal MSS bands, ten image bands and ratios, and all 48 image and map variables (less land use). Ten variable accuracy was raised over 15 percentage points from 38.4 to 53.9 percent, with the use of the 31 ancillary variables. A land-use classification map was produced with an optimal ten-channel subset of four image bands and six ancillary map variables. Point-by-point verification of 331,776 points against a 1972/1973 U.S. Geological Survey (UGSG) land-use map prepared with airphotos and the same classification scheme showed average first-, second-, and third-order accuracies of 76.3, 58.4, and 33.0 percent, respectively