Simulating Hard Rigid Bodies

Several physical systems in condensed matter have been modeled approximating their constituent particles as hard objects. The hard spheres model has been indeed one of the cornerstones of the computational and theoretical description in condensed matter. The next level of description is to consider particles as rigid objects of generic shape, which would enrich the possible phenomenology enormously. This kind of modeling will prove to be interesting in all those situations in which steric effects play a relevant role. These include biology, soft matter, granular materials and molecular systems. With a view to developing a general recipe for event-driven Molecular Dynamics simulations of hard rigid bodies, two algorithms for calculating the distance between two convex hard rigid bodies and the contact time of two colliding hard rigid bodies solving a non-linear set of equations will be described. Building on these two methods, an event-driven molecular dynamics algorithm for simulating systems of convex hard rigid bodies will be developed and illustrated in details. In order to optimize the collision detection between very elongated hard rigid bodies, a novel nearest-neighbor list method based on an oriented bounding box will be introduced and fully explained. Efficiency and performance of the new algorithm proposed will be extensively tested for uniaxial hard ellipsoids and superquadrics. Finally applications in various scientific fields will be reported and discussed.Comment: 36 pages, 17 figure

Efficient Path Planning in Narrow Passages via Closed-Form Minkowski Operations

Path planning has long been one of the major research areas in robotics, with PRM and RRT being two of the most effective classes of path planners. Though generally very efficient, these sampling-based planners can become computationally expensive in the important case of "narrow passages". This paper develops a path planning paradigm specifically formulated for narrow passage problems. The core is based on planning for rigid-body robots encapsulated by unions of ellipsoids. The environmental features are enclosed geometrically using convex differentiable surfaces (e.g., superquadrics). The main benefit of doing this is that configuration-space obstacles can be parameterized explicitly in closed form, thereby allowing prior knowledge to be used to avoid sampling infeasible configurations. Then, by characterizing a tight volume bound for multiple ellipsoids, robot transitions involving rotations are guaranteed to be collision-free without traditional collision detection. Furthermore, combining the stochastic sampling strategy, the proposed planning framework can be extended to solving higher dimensional problems in which the robot has a moving base and articulated appendages. Benchmark results show that, remarkably, the proposed framework outperforms the popular sampling-based planners in terms of computational time and success rate in finding a path through narrow corridors and in higher dimensional configuration spaces

Continuous collision detection for ellipsoids

We present an accurate and efficient algorithm for continuous collision detection between two moving ellipsoids. We start with a highly optimized implementation of interference testing between two stationary ellipsoids based on an algebraic condition described in terms of the signs of roots of the characteristic equation of two ellipsoids. Then we derive a time-dependent characteristic equation for two moving ellipsoids, which enables us to develop a real-time algorithm for computing the time intervals in which two moving ellipsoids collide. The effectiveness of our approach is demonstrated with several practical examples. © 2006 IEEE.published_or_final_versio

Quantization, Calibration and Planning for Euclidean Motions in Robotic Systems

The properties of Euclidean motions are fundamental in all areas of robotics research. Throughout the past several decades, investigations on some low-level tasks like parameterizing specific movements and generating effective motion plans have fostered high-level operations in an autonomous robotic system. In typical applications, before executing robot motions, a proper quantization of basic motion primitives could simplify online computations; a precise calibration of sensor readings could elevate the accuracy of the system controls. Of particular importance in the whole autonomous robotic task, a safe and efficient motion planning framework would make the whole system operate in a well-organized and effective way. All these modules encourage huge amounts of efforts in solving various fundamental problems, such as the uniformity of quantization in non-Euclidean manifolds, the calibration errors on unknown rigid transformations due to the lack of data correspondence and noise, the narrow passage and the curse of dimensionality bottlenecks in developing motion planning algorithms, etc. Therefore, the goal of this dissertation is to tackle these challenges in the topics of quantization, calibration and planning for Euclidean motions

Flocking for multiple ellipsoidal agents with limited communication ranges

This paper contributes a design of distributed controllers for flocking of mobile agents with an ellipsoidal shape and a limited communication range. A separation condition for ellipsoidal agents is first derived. Smooth step functions are then introduced. These functions and the separation condition between the ellipsoidal agents are embedded in novel pairwise potential functions to design flocking control algorithms. The proposed flocking design results in (1) smooth controllers despite of the agents’ limited communication ranges, (2) no collisions between any agents, (3) asymptotic convergence of each agent’s generalized velocity to a desired velocity, and (4) boundedness of the flock size, defined as the sum of all distances between the agents, by a constant

Coordination control of multiple ellipsoidal agents with collision avoidance and limited sensing ranges

This paper contributes a design of cooperative controllers that force N mobile agents with an ellipsoidal shape and a limited sensing range to track desired trajectories and to avoid collision between them. A separation condition for ellipsoidal agents is first derived. Smooth step functions are then introduced. These functions and the separation condition between the ellipsoidal agents are embedded in novel pairwise collision avoidance functions to design coordination controllers. The proposed control design guarantees (1) smooth coordination controllers despite the agents’ limited sensing ranges, (2) no collision between any agents, (3) asymptotical stability of desired equilibrium set, and (4) instability of all other undesired critical sets of the closed loop system