This study discusses kinematic and dynamic precession models for a rolling ball with a finite contact area and a point contact respectively.In literature, both conventions have been applied.In this paper, we discuss in detail the kinematic and dynamic models to describe the ball precession and the radius of a circular rolling path.The kinematic model can be used if the contact area and friction coefficient are sufficient to prevent slippage.The dynamic precession model has significance in multi-body simulation environments handling rolling balls with ideal point contacts.We have applied both the kinematic and dynamic precession model to evaluate the no-slip condition of the existing GimBall-robot.According to the result, the necessity of an external precession torque may cause slipping at lower velocities than expected if ignoring this torque., ̇ Precession rate, spin rate (rad/s) ̈ Precession acceleration of the ball (rad/s 2 ) ω Forward rolling rate of the ball (rad/s) ̇ Forward rolling acceleration (rad/s 2 ) μ Friction coefficient at contact μ a Friction coefficient share for acceleration force μ T Friction coefficient share for vertical torque

Dynamic models describing the ball-robot motion form the basis for developments in ball-robot mechanics and motion control systems. For this paper, we have conducted a literature review of decoupled forward-motion models for pendulum-driven ball-shaped robots. The existing models in the literature apply several different conventions in system definition and parameter notation. Even if describing the same mechanical system, the diversity in conventions leads into dynamic models with different forms. As a result, it is difficult to compare, reproduce and apply the models available in the literature. Based on the literature review, we reformulate all common variations of decoupled dynamic forward-motion models using a unified notation and formulation. We have verified all reformulated models through simulations, and present the simulation results for a selected model. In addition, we demonstrate the different system behavior resulting from different ways to apply the pendulum reaction torque, a variation that can be found in the literature. For anyone working with the ball-robots, the unified compilation of the reformulated dynamic models provides an easy access to the models, as well as to the related work.

To know the pose of the robot is one of the central requirements in many applications. A localization algorithm should be robust, it should give the estimate of unreliability and it should be able to recover from errors. The above requirements are often trade offs with the computational complexity. This paper presents a global localization algorithm that matches a local point map (acquired e.g. with a laser range finder) to a global map. The algorithm makes a discrete search using a best-first branch and bound method to efficiently compute the globally optimal pose estimate. Moreover, the degree of ambiguity of the pose estimate can be determined as the algorithm yields all potential pose solution candidates within the search space. Experimental results are given to show the behavior and performance analysis of the algorithm.

A real-time SLAM (simultaneous localization and mapping) approach to harvester localization and tree map generation in forest environments is presented in this paper. The method combines 2D laser localization and mapping with GPS information to form global tree maps. Building an incremental map while also using it for localization is the only way a mobile robot can navigate in large outdoor environments. Until recently SLAM has only been confined to small-scale, mostly indoor, environments. We try to addresses the issues of scale for practical implementations of SLAM in extensive outdoor environments. Presented algorithms are tested in real outdoor environments using an all-terrain vehicle equipped with the navigation sensors and a DGPS receiver.

In this paper, a method of generating a three-dimensional (3-D) geometric model for large-scale natural environments with trees is presented. The environment mapping method, which uses range images as measurement data, consists of three main phases. First, geometric feature objects are extracted from each of the range images. Second, the relative coordinate transformations (i.e., registrations) between the sensor viewpoint locations, where the range data are measured, are computed. Third, an integrated map is formed by transforming the submap data into a common frame of reference. Tree trunks visible in the range images are modeled with cylinder segments and utilized as reference features for registration computation. The final integrated 3-D model consists of the cylinder segments representing the visible sections of the tree trunks, as well as of the ground elevation data. The constructed environment map can be utilized as, for example, a virtual task environment for outdoor robotic machines such as new-generation forest working machines or service robots.