Motion Planning for Unlabeled Discs with Optimality Guarantees

We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time $\tilde{O}(m^4+m^2n^2)$, where $m$ is the number of robots and $n$ is the total complexity of the workspace. Moreover, the total length of the returned solution is at most $\text{OPT}+4m$, where OPT is the optimal solution cost. To the best of our knowledge this is the first algorithm for the problem that has such guarantees. The algorithm has been implemented in an exact manner and we present experimental results that attest to its efficiency

Coordinated Crowd Simulation With Topological Scene Analysis

This paper proposes a new algorithm to produce globally coordinated crowds in an environment with multiple paths and obstacles. Simple greedy crowd control methods easily lead to congestion at bottlenecks within scenes, as the characters do not cooperate with one another. In computer animation, this problem degrades crowd quality especially when ordered behaviour is needed, such as soldiers marching towards a castle. Similarly, in applications such as real-time strategy games, this often causes player frustration, as the crowd will not move as efficiently as it should. Also, planning of building would usually require visualization of ordered evacuation to maximize the flow. Planning such globally coordinated crowd movement is usually labour intensive. Here, we propose a simple solution that is easy to use and efficient in computation. First, we compute the harmonic field of the environment, taking into account the starting points, goals and obstacles. Based on the field, we represent the topology of the environment using a Reeb Graph, and calculate the maximum capacity for each path in the graph. With the harmonic field and the Reeb Graph, path planning of crowd can be performed using a lightweight algorithm, such that any blocking of one another's paths is minimized. Comparing to previous methods, our system can synthesize globally coordinated crowd with smooth and efficient movement. It also enables control of the crowd with high-level parameters such as the degree of cooperation and congestion. Finally, the method is scalable to thousands of characters with minimal impact to computation time. It is best applied in interactive crowd synthesis systems such as animation designs and real-time strategy games

Interactive control of multi-agent motion in virtual environments

With the increased use of crowd simulation in animation, specification of crowd motion can be very time consuming, requiring a lot of user input. To alleviate this cost, we wish to allow a user to interactively manipulate the many degrees of freedom in a crowd, whilst accounting for the limitation of low-dimensional signals from standard input devices. In this thesis we present two approaches for achieving this: 1) Combining shape deformation methods with a multitouch input device, allowing a user to control the motion of the crowd in dynamic environments, and 2) applying a data-driven approach to learn the mapping between a crowd’s motion and the corresponding user input to enable intuitive control of a crowd. In our first approach, we represent the crowd as a deformable mesh, allowing a user to manipulate it using a multitouch device. The user controls the shape and motion of the crowd by altering the mesh, and the mesh in turn deforms according to the environment. We handle congestion and perturbation by having agents dynamically reassign their goals in the formation using a mass transport solver. Our method allows control of a crowd in a single pass, improving on the time taken by previous, multistage, approaches. We validate our method with a user study, comparing our control algorithm against a common mouse-based controller. We develop a simplified version of motion data patches to model character-environment interactions that are largely ignored in previous crowd research. We design an environment-aware cost metric for the mass transport solver that considers how these interactions affect a character’s ability to track the user’s commands. Experimental results show that our system can produce realistic crowd scenes with minimal, high-level, input signals from the user. In our second approach, we propose that crowd simulation control algorithms inherently impose restrictions on how user input affects the motion of the crowd. To bypass this, we investigate a data-driven approach for creating a direct mapping between low-dimensional user input and the resulting high-dimensional crowd motion. Results show that the crowd motion can be inferred directly from variations in a user’s input signals, providing a user with greater freedom to define the animation