Continuous Alternation: The Complexity of Pursuit in Continuous Domains

Complexity theory has used a game-theoretic notion, namely alternation, to great advantage in modeling parallelism and in obtaining lower bounds. The usual definition of alternation requires that transitions be made in discrete steps. The study of differential games is a classic area of optimal control, where there is continuous interaction and alternation between the players. Differential games capture many aspects of control theory and optimal control over continuous domains. In this paper, we define a generalization of the notion of alternation which applies to differential games, and which we call "continuous alternation." This approach allows us to obtain the first known complexity-theoretic results for open problems in differential games and optimal control. We concentrate our investigation on an important class of differential games, which we call polyhedral pursuit games. Pursuit games have application to many fundamental problems in autonomous robot control in the presence of an adversary. For example, this problem occurs in manufacturing environments with a single robot moving among a number of autonomous robots with unknown control programs, as well as in automatic automobile control, and collision control among aircraft and boats with unknown or adversary control. We show that in a three-dimensional pursuit game where each player's velocity is bounded (but there is no bound on acceleration), the pursuit game decision problem is hard for exponential time. This lower bound is somewhat surprising due to the sparse nature of the problem: there are only two moving objects (the players), each with only three degrees of freedom. It is also the first provably intractable result for any robotic problem with complete information; previous intractability results have relied on complexity-theoretic assumptions. Fortunately, we can counter our somewhat pessimistic lower bounds with polynomial time upper bounds for obtaining approximate solutions. In particular, we give polynomial time algorithms that approximately solve a very large class of pursuit games with arbitrarily small error. For e > 0, this algorithm finds a winning strategy for the evader provided that there is a winning strategy that always stays at least E distance from the pursuer and all obstacles. If the obstacles are described with n bits, then the algorithm runs in time (n/e)0(1), and applies to several types of pursuit games: either velocity or both acceleration and velocity may be bounded, and the bound may be of either the L2- or L&infin-norm. Our algorithms also generalize to when the obstacles have constant degree algebraic descriptions, and are allowed to have predictable movement

Survey on Motion Planning for Multirotor Aerial Vehicles in Plan-based Control Paradigm

In general, optimal motion planning can be performed both locally and globally. In such a planning, the choice in favour of either local or global planning technique mainly depends on whether the environmental conditions are dynamic or static. Hence, the most adequate choice is to use local planning or local planning alongside global planning. When designing optimal motion planning both local and global, the key metrics to bear in mind are execution time, asymptotic optimality, and quick reaction to dynamic obstacles. Such planning approaches can address the aforesaid target metrics more efficiently compared to other approaches such as path planning followed by smoothing. Thus, the foremost objective of this study is to analyse related literature in order to understand how the motion planning, especially trajectory planning, problem is formulated, when being applied for generating optimal trajectories in real-time for Multirotor Aerial Vehicles, impacts the listed metrics. As a result of the research, the trajectory planning problem was broken down into a set of subproblems, and the lists of methods for addressing each of the problems were identified and described in detail. Subsequently, the most prominent results from 2010 to 2022 were summarized and presented in the form of a timeline

SelfPaint-A self-programming paint booth

In this paper we present a unique Fraunhofer approach that aims towards a vision to automate the product preparation in paint shops by automatically generating robot paths and process conditions that guarantee a certain wanted paint coverage. This will be accomplished through a combination of state-of-the-art simulation technology, inline quality control by novel terahertz thickness measurement technology, and surface treatment technology. The benefits of the approach are a shortened product preparation time, increased quality and reduced material and energy consumption. The painting of a tractor fender is used to demonstrate the approach

NR-RRT: Neural Risk-Aware Near-Optimal Path Planning in Uncertain Nonconvex Environments

Balancing the trade-off between safety and efficiency is of significant importance for path planning under uncertainty. Many risk-aware path planners have been developed to explicitly limit the probability of collision to an acceptable bound in uncertain environments. However, convex obstacles or Gaussian uncertainties are usually assumed to make the problem tractable in the existing method. These assumptions limit the generalization and application of path planners in real-world implementations. In this article, we propose to apply deep learning methods to the sampling-based planner, developing a novel risk bounded near-optimal path planning algorithm named neural risk-aware RRT (NR-RRT). Specifically, a deterministic risk contours map is maintained by perceiving the probabilistic nonconvex obstacles, and a neural network sampler is proposed to predict the next most-promising safe state. Furthermore, the recursive divide-and-conquer planning and bidirectional search strategies are used to accelerate the convergence to a near-optimal solution with guaranteed bounded risk. Worst-case theoretical guarantees can also be proven owing to a standby safety guaranteed planner utilizing a uniform sampling distribution. Simulation experiments demonstrate that the proposed algorithm outperforms the state-of-the-art remarkably for finding risk bounded low-cost paths in seen and unseen environments with uncertainty and nonconvex constraints

A Framework for Offline Risk-aware Planning of Low-altitude Aerial Flights during Urban Disaster Response

Disaster response missions are dynamic and dangerous events for first responders. Active situational awareness is critical for effective decision-making, and unmanned aerial assets have successfully extended the range and output of sensors. Aerial assets have demonstrated their capability in disaster response missions via decentralized operations. However, literature and industry lack a systematic investigation of the algorithms, datasets, and tools for aerial system trajectory planning in urban disasters that optimizes mission performance and guarantee mission success. This work seeks to develop a framework and software environment to investigate the requirements for offline planning algorithms and flight risk models when applied to aerial assets exploring urban disaster zones. This is addressed through the creation of rapid urban maps, efficient flight planning algorithms, and formal risk metrics that are demonstrated in scenario-driven experiments using Monte Carlo simulation. First, rapid urban mapping strategies are independently compared for efficient processing and storage through obstacle and terrain layers. Open-source data is used when available and is supplemented with an urban feature prediction model trained on satellite imagery using deep learning. Second, sampling-based planners are evaluated for efficient and effective trajectory planning of nonlinear aerial dynamic systems. The algorithm can find collision-free, kinodynamic feasible trajectories using random open-loop control targets. Alternative open-loop control commands are formed to improve the planning algorithm’s speed and convergence. Third, a risk-aware implementation of the planning algorithm is developed that considers the uncertainty of energy, collisions, and onboard viewpoint data and maps them to a single measure of the likelihood of mission failure. The three modules are combined in a framework where the rapid urban maps and risk-aware planner are evaluated against benchmarks for mission success, performance, and speed while creating a unique set of benchmarks from open-source data and software. One, the rapid urban map module generates a 3D structure and terrain map within 20 meters of data and in less than 5 minutes. The Gaussian Process terrain model performs better than B-spline and NURBS models in small-scale, mountainous environments at 10-meter squared resolution. Supplementary data for structures and other urban landcover features is predicted using the Pix2Pix Generative Adversarial Network with a 3-channel encoding for nine labels. Structures, greenspaces, water, and roads are predicted with high accuracy according to the F1, OIU, and pixel accuracy metrics. Two, the sampling-based planning algorithm is selected for forming collision-free, 3D offline flight paths with a black-box dynamics model of a quadcopter. Sampling-based planners prove successful for efficient and optimal flight paths through randomly generated and rapid urban maps, even under wind and noise uncertainty. The Stable-Sparse-RRT, SST, algorithm is shown to improve trajectories for minimum Euclidean distance more consistently and efficiently than the RRT algorithm, with a 50% improvement in finite-time path convergence for large-scale urban maps. The forward propagation dynamics of the black-box model are replaced with 5-15 times more computationally efficient motion primitives that are generated using an inverse lower-order dynamics model and the Differential Dynamic Programming, DDP, algorithm. Third, the risk-aware planning algorithm is developed that generates optimal paths based on three risk metrics of energy, collision, and viewpoint risk and quantifies the likelihood of worst-case events using the Conditional-Value-at-Risk, CVaR, metric. The sampling-based planning algorithm is improved with informative paths, and three versions of the algorithm are compared for the best performance in different scenarios. Energy risk in the planning algorithm results in 5-35% energy reduction and 20-30% more consistency in finite-time convergence for flight paths in large-scale urban maps. All three risk metrics in the planning algorithm generally result in more energy use than the planner with only energy risk, but reduce the mean flight path risk by 10-50% depending on the environment, energy available, and viewpoint landmarks. A final experiment in an Atlanta flooding scenario demonstrates the framework’s full capability with the rapid urban map displaying essential features and the trajectory planner reporting flight time, energy consumption, and total risk. Furthermore, the simulation environment provides insight into offline planning limitations through Monte Carlo simulations with environment wind and system dynamics noise. The framework and software environment are made available to use as benchmarks in the field to serve as a foundation for increasing the effectiveness of first responders’ safety in the challenging task of urban disaster response.Ph.D

Implications of Motion Planning: Optimality and k-survivability

We study motion planning problems, finding trajectories that connect two configurations of a system, from two different perspectives: optimality and survivability. For the problem of finding optimal trajectories, we provide a model in which the existence of optimal trajectories is guaranteed, and design an algorithm to find approximately optimal trajectories for a kinematic planar robot within this model. We also design an algorithm to build data structures to represent the configuration space, supporting optimal trajectory queries for any given pair of configurations in an obstructed environment. We are also interested in planning paths for expendable robots moving in a threat environment. Since robots are expendable, our goal is to ensure a certain number of robots reaching the goal. We consider a new motion planning problem, maximum k-survivability: given two points in a stochastic threat environment, find n paths connecting two given points while maximizing the probability that at least k paths reach the goal. Intuitively, a good solution should be diverse to avoid several paths being blocked simultaneously, and paths should be short so that robots can quickly pass through dangerous areas. Finding sets of paths with maximum k-survivability is NP-hard. We design two algorithms: an algorithm that is guaranteed to find an optimal list of paths, and a set of heuristic methods that finds paths with high k-survivability

Enhanced online programming for industrial robots

The use of robots and automation levels in the industrial sector is expected to grow, and is driven by the on-going need for lower costs and enhanced productivity. The manufacturing industry continues to seek ways of realizing enhanced production, and the programming of articulated production robots has been identified as a major area for improvement. However, realizing this automation level increase requires capable programming and control technologies. Many industries employ offline-programming which operates within a manually controlled and specific work environment. This is especially true within the high-volume automotive industry, particularly in high-speed assembly and component handling. For small-batch manufacturing and small to medium-sized enterprises, online programming continues to play an important role, but the complexity of programming remains a major obstacle for automation using industrial robots. Scenarios that rely on manual data input based on real world obstructions require that entire production systems cease for significant time periods while data is being manipulated, leading to financial losses. The application of simulation tools generate discrete portions of the total robot trajectories, while requiring manual inputs to link paths associated with different activities. Human input is also required to correct inaccuracies and errors resulting from unknowns and falsehoods in the environment. This study developed a new supported online robot programming approach, which is implemented as a robot control program. By applying online and offline programming in addition to appropriate manual robot control techniques, disadvantages such as manual pre-processing times and production downtimes have been either reduced or completely eliminated. The industrial requirements were evaluated considering modern manufacturing aspects. A cell-based Voronoi generation algorithm within a probabilistic world model has been introduced, together with a trajectory planner and an appropriate human machine interface. The robot programs so achieved are comparable to manually programmed robot programs and the results for a Mitsubishi RV-2AJ five-axis industrial robot are presented. Automated workspace analysis techniques and trajectory smoothing are used to accomplish this. The new robot control program considers the working production environment as a single and complete workspace. Non-productive time is required, but unlike previously reported approaches, this is achieved automatically and in a timely manner. As such, the actual cell-learning time is minimal

Heterogeneous Dimensionality Reduction for Efficient Motion Planning in High-Dimensional Spaces

© 2013 IEEE. Increasing the dimensionality of the configuration space quickly makes trajectory planning computationally intractable. This paper presents an efficient motion planning approach that exploits the heterogeneous low-dimensional structures of a given planning problem. These heterogeneous structures are obtained via a Dirichlet process (DP) mixture model and together cover the entire configuration space, resulting in more dimensionality reduction than single-structure approaches from the existing literature. Then, a unified low-dimensional trajectory optimization problem is formulated based on the obtained heterogeneous structures and a proposed transversality condition which is further solved via SQP in our implementation. The positive results demonstrate the feasibility and efficiency of our trajectory planning approach on an autonomous underwater vehicle (AUV) and a high-dimensional intervention autonomous underwater vehicle (I-AUV) in cluttered 3D environments