Modular Serial Robot Dynamics

This paper deals with the concept of reconfigur-able and self reconfigurable robots. These robots are in-tended to be used as a main component of intelligent manufacturing systems. The paper presents basic concepts of this type of robots, kinematical methods used to build virtual models, numerical results and virtual models. Also, conclusions are at the end.

Abstract. The applications and understanding of Land-use Regulations (LuR) are more communicable when they are linked to the digital representation of the physical world. In order to support issuing a planning permit and move towards the establishment of automated planning permit checks, this paper investigates how LuRs related to a planning permit process can be modelled in 3D called 3D CityLuR. 3D CityLuR serves as a 3D model for representing LuRs’ legal extents on a city scale. It is formed based on multiple geometric modelling approaches representing LuRs, which can provide a better cognitive understanding of LuRs and subsequently facilitate LuR automatic checks. To this purpose, according to LuRs’ descriptions and characteristics explained in related planning documents, key parameters representing LuRs’ extent are identified (e.g. maximum distance in overlooking or maximum allowed height in building height regulations). Accordingly, to automatically model each LuR, a geometric modelling approach (e.g. Boundary Representation (B-Rep), CSG, and extrusion) that best fits with the identified key parameters is proposed. In addition, to combine 3D CityLuR with an integrated BIM-GIS environment, the level of information need in terms of geometries and semantics is specified. Finally, the paper results in a showcase for five LuRs including building height, energy efficiency protection, overshadowing open space, overlooking, and noise impacts regulations. The showcase is a proof of concept for determining how these LuRs can be modelled in 3D and combined with 3D city models based on the selected geometric modelling approaches, identified parameters, and level of information need.

A new geometric error modeling approach for multi-axis system based on stream of variation theory

This paper presents a novel 6-URS self-reconfigurable all-dimensional walking robot. The model of the 6-URS self-reconfigurable walking robot is established, then its reconfiguration modes are proposed. Based on the screw theory, the degrees of freedom (DOF) of this robot before and after reconfiguration are analysed separately to verify the feasibility of self-reconfiguration. This robot can achieve self-reconfigurable function with the design of self-reconfigurable limbs. Moreover, the trajectory planning and simulation of three kinds of gaits are performed, including walking horizontally, turning and climbing. The above analysis shows that the 6-URS self-reconfigurable all-dimensional robot satisfies the walking requirements and has the reconfigurable ability in unstrcutured environment.

The modeling of a modular robot system is complex due to its capability of changing and forming countless robot configurations with a set of modules. The greater the number of modules added to the structure, more complicated is the robot and its modeling. A methodology to represent modular robot configurations as a fixed shape robot is presented. The equivalent model is obtained through the characterization of the module, graph theory and geometric modeling of robots. After the transformation, the resulting kinematic and dynamic parameters are similar to the traditional model of a single configuration robot. Once the equivalent model is obtained, it can be used within different robot applications.

Project critical mission requirements often drive design decisions and processes. This was the case for National Aeronautics and Space Administration (NASA) funded DEep Phreatic THermal eXplorer (DepthX), an underwater robot designed to autonomously map, navigate, and acquire biological samples. Mission requirements led the authors to develop a novel core sampling mechanism for variable density materials. Preliminary testing was conducted on variable density materials simulating real world specimens to identify the series of motions to acquire an acceptable core and optimize the geometry of the coring tube. A geometric modeling approach with configuration functions was employed to design the overall mechanism and establish the cam profile. The design was tested and evaluated during multiple field expeditions to cenotes (sinkholes) in Mexico. The culmination of the preliminary testing and the selected design methodology resulted in a core sampling mechanism that is compact, has minimal operational torque requirements, and utilizes a single motor to complete a series of complex functions. Future applications are envisioned for space expeditions, underwater exploration, and medical sampling.

We present a new method of defining spatio-temporal clusters using the geometric modeling approach, which simulates the phenomenon (clustered multi-ray arrivals) that has a geometric analog. As such, various clusters are given different shapes to scatterer distributions based on their logical appeal to certain radio environments. This classification methodology is based on the semi-geometrically based statistical model developed in the previous work. Subsequently, the analytical expression of the cluster power is derived using the proposed model. As a test case, we further give the expression of weightage of cluster power for a Gaussian scatterer density model, where scatterers have a normal distribution of the x- and y-coordinates measured from the position of the mobile station. We also study the effect of this weightage on the average received power at the base station when directive antennas are implemented at the receiver using computer simulation. Finally the probability distribution function of the weightage of the apparent-cluster power in a generalized rural area are analyzed by assuming that the distribution of the apparent clusters has an exponentially decaying function in the radial distance and a uniform function in azimuth.

Hydrogen-bonding interactions often make substantial contributions to the specificity of protein-nucleic acid complexes. Using a geometric modeling approach, we previously identified 28 possible doubly hydrogen-bonded interactions to the four unpaired RNA bases. Here we present interaction energies of these models, calculated by ab initio quantum chemical methods, and describe a correlation between the computed energies and observed frequencies of the interactions. In general, interactions with charged side chains show the most favorable energies. An Asp/Glu-G interaction may be especially favorable for recognition of unpaired guanines in RNAs. Asn and Ser/Thr/Tyr side chains are calculated to make iso-energetic interactions to the Hoogsteen face of adenine, but Asn-A interactions are much more common with DNA than RNA, and Ser/Thr/Tyr-A interactions are more common with RNA than DNA. Examination of the known interactions suggests that Ser/Thr/Tyr may be accommodated in a wider variety of protein contexts at RNA-protein interfaces. With these calculated intrinsic affinities, it should be possible to better assess the contributions of bidentate hydrogen-bonding interactions to RNA- and DNA-binding specificity.

Size distribution of free particles in soils: a geometric modelling approach

Sustainable biomineralization technologies rely on the efficient hydrolysis of urea, typically catalyzed by urease-producing microorganisms or purified enzymes. However, conventional approaches such as microbially induced calcium carbonate precipitation (MICP) and enzyme induced calcium carbonate precipitation (EICP) face limitations related to biosafety risks and high costs, respectively. In this study, soybean, an abundant and low-cost agricultural resource, was utilized to extract urease through a soaking and centrifugation process. A geometric modeling approach using tri-axial ellipsoid theory was introduced to explain how soybean grain size affects sieved powder yield. The effects of soybean grain size, powder concentration, temperature, pH, and storage conditions on the urease activity were systematically evaluated. Results showed that smaller soybean particle sizes resulted in lower extraction efficiency, whereas medium-grain soybeans provided the most cost-effective source due to their higher sieved powder yield and lower market price. Urease activity was positively correlated with both powder concentration and temperature within the tested range and reached its maximum at approximately pH 8. Additionally, storage at 4 °C significantly preserved the enzyme's initial activity over 72 h compared to room temperature conditions. These findings establish a practical foundation for the cost-effective production of plant-derived urease, promoting broader application of biomineralization techniques in sustainable geotechnical engineering.

This chapter reviews the basic concepts, definitions, and algorithms in graph theory, which is important to the mathematical representation of modular robot assembly configurations. Since a modular robot is a collection of link and joint modules, a re-classification scheme for links and joints is proposed to translate a modular robot into a kinematic graph. Finally, the modified Assembly Incidence Matrix (AIM) is introduced to fully describe the assembly configuration of a modular robot in a compact matrix form, which makes the automatic generation of the kinematic, dynamic, and calibration models more convenient.

The ability of reconfiguration makes modular robots have the ability of adaptable, low-cost, self-healing and fault-tolerant. It can also be applied to a variety of mission situations. In this manuscript, a robot platform which relied on the module library was designed, based on the screw theory and module theory. Then, the configuration design method of the modular robot was proposed. And the different configurations of modular robot system have been built, including industrial mechanical arms, the mobile platform, six-legged robot and 3D exoskeleton manipulator. Finally, the simulation and verification of one system among them have been made, using the analyses of screw kinematics and polynomial planning. The results of experiments demonstrate the feasibility and superiority of this modular system.

Highly redundant modular robots may undergo large shape changes which significantly affect the geometry and dynamics of the robot. In these motions, the shape change may induce a tipping or rolling behavior of the robot. The paper describes the dynamic modeling, locomotion planning, control and simulation of such rolling motions for the Tetrobot modular robots. The motion is described by the path profiles of controlled nodes, the tipping criteria and dynamic tipping motion and an impact-reaction model of contact with the ground. These phases of motion are described using Newton-Euler dynamic equations and the principle of conservation of angular momentum. In the paper, a two-phase planning and switching control sequence is introduced to achieve stable and reliable motion of a Tetrobot modular robot. Simulation results illustrate the tipping behavior of a tetrahedron, the dynamic contact and rolling of an icosahedral Tetrobot and dynamic control of the rolling Tetrobot. The resulting models are useful to analyze and control both intentional rolling as a new mode of mobility as well as the avoidance of unintentional tipping and rolling during task execution.

Abstract. Porches, as defined by the Art & Architecture Thesaurus, serve as vital transitional spaces linking indoor and outdoor environments. Despite their historical and contemporary significance, porches lack explicit representation in prevalent standards like CityGML and IndoorGML, posing challenges for comprehensive spatial modeling and its application. This paper proposes a method for modeling porches that aligns with the existing OGC standard CityGML 3.0, ensuring accuracy and compatibility. Drawing upon geomatics techniques, the method aims to bridge the gap in representing these spaces, critical for applications such as navigation systems, urban planning, and energy simulations. By integrating geometric, machine learning, and informative modeling approaches, this method seeks to provide a robust foundation for various practical applications. The paper outlines a comprehensive state-of-the-art review, describes the proposed method from digitalization to random forest (RF)-based point cloud classification and vectorization, presents case studies and results, and offers critical discussions and conclusions. Through this endeavor, the paper contributes to enhancing the representation and understanding of porches within the digital spatial landscape.

An approach for geometric error modeling of parallel manipulators (PMs) based on the visual representation and direct calculation of conformal geometric algebra is introduced in this paper. In this method, the finite motion of an open-loop chain is firstly formulated. Through linearization of the finite motion, error propagation of the open-loop chain is analyzed. Then the error sources are separated in terms of joint perturbations and geometric errors. Next, motions and constraints of PMs are analyzed visually by their reciprocal property. Finally geometric error model of PMs are formulated considering the actuations and constraints. The merits of this new approach are twofold: (1) complete and continuous geometric error modeling can be achieved since finite motions are considered, (2) visual and analytical computation of motions and constraints are applied for transferring geometric errors from the open-loop chain to the PM. A 2-DoF rotational PM is applied to demonstrate the geometric error modeling process. Comparisons between simulation and analytical models show that this approach is highly effective.