Publications of Roland Geraerts

Space-time Group Motion Planning

Wed, 25 Apr 2012 7:40:00 GMT

We present a novel approach for planning and directing heterogeneous groups of virtual agents based on techniques from linear programming. Our method efficiently identifies the most promising paths in both time and space and provides an optimal distribution of the groups’ members over these paths such that their average traveling time is minimized. The computed space-time plan is combined with an agent-based steering method to handle collisions and generate the final motions of the agents. Our overall solution is applicable to a variety of virtual environment applications, such as computer games and crowd simulators. We highlight its potential through a wide range of test-case scenarios and evaluate the results from our simulations using a number of quantitative quality metrics. In practice, our system runs at interactive rates and generates smooth and optimal crowd flows under a variety of conditions.

A Navigation Mesh for Dynamic Environments

Wed, 29 Feb 2012 10:15:00 GMT

Games and simulations frequently model scenarios where obstacles move, appear, and disappear in an environment. A city environment changes as new buildings and roads are constructed, and routes can become partially blocked by small obstacles many times in a typical day. This paper studies the effect of using local updates to repair only the affected regions of a navigation mesh in response to a change in the environment. The techniques are inspired by incremental methods for Voronoi diagrams. Experiments show that local updates are fast enough to permit real-time updates of the navigation mesh. The main novelty of this paper is that we show how to maintain a 2D or 2.5D navigation mesh in an environment that contains dynamic polygonal obstacles.

Real-Time Density-Based Crowd Simulation

Wed, 18 Jan 2012 8:50:00 GMT

Virtual characters in games and simulations often need to plan visually convincing paths through a crowded environment. This paper describes how crowd density information can be used to guide a large number of characters through a crowded environment. Crowd density information helps characters avoid congested routes that could lead to traffic jams. It also encourages characters to use a wide variety of routes to reach their destination.

Our technique measures the desirability of a route by combining distance information with crowd density information. We start by building a navigation mesh for the walkable regions in a polygonal 2D or multi-layered 3D environment. The skeleton of this navigation mesh is the medial axis. Each walkable region in the navigation mesh maintains an up-to-date density value. This density value equals the area of all characters inside a given region divided by the total area of this region. These density values are mapped onto the medial axis to form a weighted graph. An A* search on this graph yields a backbone path for each character, and forces are used to guide the characters through the weighted environment. The characters periodically replan their routes as the density values are updated. Our experiments show that we can compute congestion-avoiding paths for tens of thousands of characters in real-time.

Standards in Virtual Worlds Virtual Travel Use Case Metaverse1 Project

Fri, 30 Dec 2011 10:30:00 GMT

Nowadays, tourism has become a very important industry in the international economy. Information and communication technologies are in constant development; they progress worldwide and across sectors. Their applications in tourism and tourist resources is rapidly increasing, reaching new, innovative and sometimes amazing results in terms of effectiveness, productivity, quality, and customer satisfaction. Exploring the interaction between technologies and tourism is difficult and challenging. Specifically, using virtual world technologies as a new means of information for potential tourists is a big challenge where the actual methods, goals and needs still need to be exactly identified.

This paper aims at analyzing why and how virtual worlds can become an important platform for tourism-oriented areas to promote a destination in general, and their local heritage and tourist addedvalue services in particular. The document will also introduce the design of the first prototypes and the validation results of the four specific technologies tested at the Virtual Travel Use Case (Soundscape generation, Multilinguality, Video streaming and Path and Camera Planning). Finally, the contribution to the MPEG-V standard will also be detailed in the paper.

Navigation Meshes for Realistic Multi-Layered Environments

Fri, 15 Jul 2011 14:20:00 GMT

Virtual characters often need to plan visually convincing paths through a complicated environment. For example, a traveler may need to walk from an airport entrance to a staircase, descend the staircase, walk to a shuttle, ride the shuttle to a destination, ride an elevator back to the ground floor, and finally move on the ground floor again to reach the desired airplane. Most previous research only supports path planning in a single plane because the underlying data structures are twodimensional. The goal of this paper is to permit visually convincing paths to be efficiently computed in a multilayered environment such as an airport or a multi-storey building. We describe an algorithm to create a navigation mesh, and our implementation demonstrates the feasibility of the approach.

A multi-layered environment is represented by a set of two-dimensional layers and a set of connections. Each layer is a collection of two-dimensional polygons that all lie in a single plane, and each connection provides a means of moving between layers.

We first compute the traditional medial axis of each two-dimensional layer in the environment. The connections are then used to iteratively merge this collection of medial axes into a single data structure. By adding a linear number of line segments to this structure, we obtain a navigation mesh that mathematically describes the walkable areas in a multi-layered environment. This mesh can easily be input into existing planners to generate visually convincing paths for thousands of virtual characters in real-time.

Combining Path Planners and Motion Graphs

Thu, 24 Feb 2011 12:00:00 GMT

Natural locomotion of virtual characters is very important in games and simulations. The naturalness of the total motion strongly depends on both the path the character chooses and the animation of the walking character. Therefore, much work has been done on path planning and generating walking animations. However, the combination of both fields has received less attention. Combining path planning and motion synthesis introduces several problems. In this paper, we will identify two problems and propose possible solutions.

The first problem is selecting an appropriate distance metric for locomotion synthesis. When concatenating clips of locomotion, a distance metric is required to detect good transition points. We have evaluated three common distance metrics both quantitatively (in terms of footskating, path deviation and online running time) and qualitatively (user study). Based on our observations, we propose a set of guidelines when using these metrics in a motion synthesizer.

The second problem is the fact that there is no single point on the body that can follow the path generated by the path planner without causing unnatural animations. This raises the question how the character should follow the path. We will show that enforcing the pelvis to follow the path will lead to unnatural animations and that our proposed solution, which uses path abstractions, generates significantly better animations.

Path Planning for Groups using Column Generation

Fri, 27 Aug 2010 14:00:00 GMT

In computer games, one or more groups of units need to move from one location to another as quickly as possible. If there is only one group, then it can be solved efficiently as a dynamic flow problem. If there are several groups with different origins and destinations, then the problem becomes NP-hard. In current games, these problems are solved by using greedy ad hoc rules, leading to long traversal times or congestions and deadlocks near narrow passages. We present a centralized optimization approach based on Integer Linear Programming. Our solution provides an efficient heuristic to minimize the average and latest arrival time of the units.

Stealth-Based Path Planning using Corridor Maps

Mon, 29 Mar 2010 15:00:00 GMT

A relatively new area within the field of path planning deals with computing a stealthy path for a character moving in a virtual environment. Besides efficiently obtaining a path that is collision-free, short and smooth, the added difficulty is that the path must have little or no exposure to observers. We propose a new algorithm for computing such a path in the plane, and show that real-time performance can be achieved.

Planning Short Paths with Clearance using Explicit Corridors

Fri, 29 Jan 2010 15:00:00 GMT

A central problem of applications dealing with virtual environments is planning a collision-free path for a character. Since environments and their characters are growing more realistic, a character’s path needs to be visually convincing, meaning that the path is smooth, short, has some clearance to the obstacles in the environment, and avoids other characters. Up to now, it has proved difficult to meet these criteria simultaneously and in real-time.

We introduce a new data structure, i.e. the Explicit Corridor Map, which allows creating the shortest path, the path that has the largest amount of clearance, or any path in between. Besides being efficient, the corresponding algorithms are surprisingly simple. By integrating the data structure and algorithms into the Indicative Route Method, we show that visually convincing short paths can be obtained in real-time.

Camera Planning in Virtual Environments using the Corridor Map Method

Tue, 17 Nov 2009 15:00:00 GMT

Planning high-quality camera motions is a challenging problem for applications dealing with interactive virtual environments. This challenge is caused by conflicting requirements. On the one hand we need good motions, formed by trajectories that are collision-free and keep the character that is being followed in clear view. On the other hand, we need frame coherence, i.e. the view must change smoothly such that the viewer does not get disoriented. Since camera motions dynamically evolve, good motions may require the camera to jump, leading to a broken frame coherence. Hence, a careful trade-off must be made. In addition to this challenge, interactive applications require real-time computations, preventing an exhaustive search for `the best' solution.

We propose a new method for planning camera motions which tackles this trade-off in real-time. The method can be used for planning camera motions of NPC's and first-person characters. Experiments show that high-quality camera motions are obtained for both scenarios in real-time.

Indicative Routes for Path Planning and Crowd Simulation

Tue, 12 May 2009 15:00:00 GMT

An important challenge in virtual environment applications is to steer virtual characters through complex and dynamic worlds. The characters should be able to plan their paths and move toward their desired locations, avoiding at the same time collisions with the environment and with other moving entities. In this paper we propose a general method for realistic path planning, the Indicative Route Method (irm). In the irm, a so-called indicative route determines a global route for the character, whereas a corridor around this route is used to handle a broad range of other path planning issues, such as avoiding characters and computing smooth paths. As we will show, our method can be used for real-time navigation of many moving characters in complicated environments. It is fast, flexible and generates believable paths.

Using the Corridor Map Method for Path Planning for a Large Number of Characters

Tue, 11 Nov 2008 15:00:00 GMT

Path planning is a central problem in virtual environments and games. When computer-controlled characters move around in virtual worlds they have to plan their paths to desired locations. These paths must avoid collisions with the environment and with other moving characters. Also a chosen path must be natural, meaning that it is the kind of path a real human being could take. The algorithms for planning such paths must be able to handle hundreds of characters in real-time and must be flexible.

The Corridor Map Method (cmm) was recently introduced as a flexible path planning method in interactive virtual environments and games. The method is fast and flexible and the resulting paths are reasonable. However, the paths tend to take unnatural turns when characters get close to other characters or small obstacles. In this paper we will improve on the cmm by decoupling collision avoidance with the environment and local steering behavior. The result is a method that keeps the advantages of the cmm but has much more natural steering. Also the method allows for more flexibility in the desired routes of the characters.

Enhancing Corridor Maps for Real-Time Path Planning in Virtual Environments

Tue, 15 Jul 2008 15:00:00 GMT

A central problem in interactive virtual environments is planning high-quality paths for characters avoiding obstacles in the environment. Current applications require a path planner that is fast (to ensure real-time interaction with the environment) and flexible (to avoid local hazards). In addition, paths need to be natural, i.e. smooth and short.

To satisfy these requirements, we need an adequate representation of the free space stored in a convenient data structure, a fast mechanism for querying this data structure, and an algorithm that constructs natural paths for the characters.

We improve an existing data structure, the Corridor Map, which represents the free space by a graph whose edges correspond to collision-free corridors. We show that this structure, together with a kd-tree, can be used for fast querying, resulting in a corridor that guides the global path of the character. Its local motions are controlled by force functions, providing the desired flexibility. Experiments show that the improvements lead to a method which can steer a crowd of approximately 10,000 characters in real-time.

Flexible Path Planning Using Corridor Maps

Fri, 4 Jul 2008 15:00:00 GMT

The Corridor Map Method: A General Framework for Real-Time High-Quality Path Planning

Thu, 5 Apr 2007 15:00:00 GMT

In many virtual environment applications, paths have to be planned for characters to traverse from a start to a goal position in the virtual world while avoiding obstacles. Contemporary applications require a path planner that is fast (to ensure real-time interaction with the environment) and flexible (to avoid local hazards such as small and dynamic obstacles). In addition, paths need to be smooth and short to ensure natural looking motions.

Current path planning techniques do not obey these criteria simultaneously. For example, A* approaches generate unnatural looking paths, potential field-based methods are too slow, and sampling-based path planning techniques are inflexible. We propose a new technique, the Corridor Map Method (CMM), which satisfies all criteria. In an off-line construction phase, the CMM creates a system of collision-free corridors for the static obstacles in an environment. In the query phase, paths can be planned inside the corridors for different types of characters while avoiding dynamic obstacles. Experiments show that high-quality paths for single characters or groups of characters can be obtained in real-time.

The Corridor Map Method: Real-Time High-Quality Path Planning

Wed, 7 Feb 2007 15:00:00 GMT

A central problem in robotics is planning a collision-free path for a moving object in an environment with obstacles. Contemporary applications require a path planner that is fast (to ensure real-time interaction with the environment) and flexible (to avoid local hazards). In addition, paths need to be smooth and short. We propose a new framework, the Corridor Map Method, which meets these requirements.

Reachability-based Analysis for Probabilistic Roadmap Planners

Wed, 16 Jul 2008 15:00:00 GMT

In the last fifteen years, sampling-based planners like the Probabilistic Roadmap Method (PRM) have proved to be successful in solving complex motion planning problems. While theoretically, the complexity of the motion planning problem is exponential in the number of degrees of freedom, sampling-based planners can successfully handle this curse of dimensionality in practice. We give a reachability-based analysis for these planners which leads to a better understanding of the success of the approach. This analysis compares the techniques based on coverage and connectivity of the free configuration space. The experiments show, contrary to general belief, that the main challenge is not getting the free space covered but getting the nodes connected, especially when the problems get more complicated, e.g. when a narrow passage is present. By using this knowledge, we can tackle the narrow passage problem by incorporating a refined neighbor selection strategy, a hybrid sampling strategy, and a more powerful local planner, leading to a considerable speed-up.

Creating High-Quality Paths for Motion Planning

Wed, 16 Jul 2008 15:00:00 GMT

Many algorithms have been proposed that create a path for a robot in an environment with obstacles. Most methods are aimed at finding a solution. However, for many applications, the path must be of a good quality as well. That is, a path should be short and should keep some amount of minimum clearance to the obstacles. Traveling along such a path reduces the chances of collisions due to the difficulty of measuring and controlling the precise position of the robot.

This paper reports a new technique, called Partial shortcut, which decreases the path length. While current methods have difficulties in removing all redundant motions, the technique efficiently removes these motions by interpolating one degree of freedom at a time.

Two algorithms are also studied that increase the clearance along paths. The first one is fast but can only deal with rigid, translating bodies. The second algorithm is slower but can handle a broader range of robots, including three-dimensional free-flying and articulated robots, which may reside in arbitrary high-dimensional configuration spaces. A big advantage of these algorithms is that clearance along paths can now be increased efficiently without using complex data structures and algorithms.

Finally, we combine the two criteria and show that high-quality paths can be obtained for a broad range of robots.

Sampling-based Motion Planning: Analysis and Path Quality

Mon, 8 May 2006 11:45:00 GMT

One of the fundamental tasks robots have to perform is planning their motions while avoiding collisions with obstacles in the environment. This is the central topic of the thesis. We restrict ourselves to motion planning for two- and three-dimensional rigid bodies and articulated robots moving in static and known virtual environments.

This thesis has been divided into two parts. The first part deals with comparing and analyzing sampling-based motion planning techniques, in particular variants of the Probabilistic Roadmap Method (PRM). The PRM consists of two phases: a construction and a query phase. In the construction phase, a roadmap (graph) is built, approximating the motions that can be made in the environment. First, a free random sample is created. Such a sample describes a particular placement of the moving object (robot) in the workspace. Then, a simple local planner is employed to connect the sample to some neighbors. Samples and connections are added to the graph until the roadmap is dense enough. In the query phase, the start and goal samples are connected to the graph. The path is obtained by a Dijkstra's shortest path algorithm.

Many variants of the PRM have been developed over the past decade. Using both time-based as well as reachability-based analysis, we compare some of the most prominent techniques. The results are surprising in the sense that techniques often perform differently than claimed by the designers. In addition, contrary to general belief, the main challenge is not getting the free space covered but getting the nodes connected, especially when the problems get more complicated, e.g. when a narrow passage is present. By using this knowledge, we can tackle the narrow passage problem by incorporating a more powerful local planner, a refined neighbor selection strategy and a hybrid sampling strategy. The analysis also shows why the PRM successfully deals with many motion planning problems.

The second part deals with quality aspects of paths and roadmaps. A good path is relatively short, keeps some distance (clearance) from the obstacles, and is smooth. We will provide algorithms that increase path clearance. A big advantage of these algorithms is that high-clearance paths can now be efficiently created without using complex data structures and algorithms. We also elaborate on algorithms that successfully decrease path length. Then, we introduce the Reachability Roadmap Method which creates small roadmaps for two- and three-dimensional problems. Such a small roadmap has many advantages over a roadmap that is created by the PRM. In particular, the method assures low query times, low memory consumption, and the roadmap can be optimized easily. The algorithm also ensures that a path is always found (if one exists) at a given resolution. We unify the techniques to create high-quality roadmaps for interactive virtual environments. That is, we use the Reachability Roadmap Method to create an initial roadmap. We add useful cycles to provide alternative routes and short paths, and we add clearance to the roadmap to obtain high-clearance paths in real-time.

A Comparative Study of Probabilistic Roadmap Planners

Sun, 15 Dec 2002 16:00:00 GMT

The probabilistic roadmap approach is a commonly used motion planning technique. A crucial ingredient of the approach is a sampling algorithm that samples the configuration space of the moving object for free configurations. Over the past decade many sampling techniques have been proposed. It is difficult to compare the different techniques because they were tested on different types of scenes, using different underlying libraries, implemented by different people on different machines. We compared twelve of such sampling techniques within a single environment on the same scenes. The results were surprising in the sense that techniques often performed differently than claimed by the designers. The study also showed how difficult it is to evaluate the quality of the techniques. The results should help users in deciding which technique is suitable for their situation.