A Reduced and Linearized High Fidelity Waveboard Multibody Model for Stability Analysis

In this paper, the stability of a waveboard, a human propelled two-wheeled vehicle consisting in two rotatable platforms, joined by a torsion bar and supported on two caster wheels, is analysed. A multibody model with holonomic and nonholonomic constraints is used to describe the system. The nonlinear equations of motion, which constitute a Differential-Algebraic system of equations (DAE system), are linearized along the steady forward motion resorting to a recently validated linearization procedure, which allows the maximum possible reduction of the linearized equations of motion of constrained multibody systems. The approach enables the generation of the Jacobian matrix in terms of the geometric and dynamic parameters of the multibody system, and the eigenvalues of the system are parameterized in terms of the design parameters. The resulting minimum set of linear equations leads to the elimination of spurious null eigenvalues, while retaining all the stability information in spite of the reduction of the Jacobian matrix. The linear stability results of the waveboard obtained in previous work are validated with this approach. The procedure shows an excellent computational efficiency with the waveboard, its utilization being highly advisable to linearize the equations of motion of complex constrained multibody systems.

Pure rolling motion of hyperquadrics in pseudo-Euclidean spaces

<p style='text-indent:20px;'>This paper is devoted to rolling motions of one manifold over another of equal dimension, subject to the nonholonomic constraints of no-slip and no-twist, assuming that these motions occur inside a pseudo-Euclidean space. We first introduce a definition of rolling map adjusted to this situation, which generalizes the classical definition of Sharpe [<xref ref-type="bibr" rid="b26">26</xref>] for submanifolds of an Euclidean space. We also prove some important properties of these rolling maps. After presenting the general framework, we analyse the particular rolling of hyperquadrics embedded in pseudo-Euclidean spaces. The central topic is the rolling of a pseudo-hyperbolic space over the affine space associated with its tangent space at a point. We derive the kinematic equations, as well as the corresponding explicit solutions for two specific cases, and prove the existence of a rolling map along any curve in that rolling space. Rolling of a pseudo-hyperbolic space on another and rolling of pseudo-spheres are equally treated. Finally, for the central theme, we write the kinematic equations as a control system evolving on a certain Lie group and prove its controllability. The choice of the controls corresponds to the choice of a rolling curve.</p>

Time-Varying Formation Control for Heterogeneous Planar Underactuated Multi-Vehicle Systems

This paper presents a distributed control approach for time-varying formation of heterogeneous planar underactuated vehicle networks without global position measurements. All vehicles in the network are modeled as generic three degree of freedom planar rigid bodies with two control inputs, and are allowed to have non-identical dynamics. Feasible trajectories are generated for each vehicle using the nonholonomic constraints of the vehicle dynamics. By exploiting the cascaded structure of the planar vehicle model, a transformation is introduced to define the reduced order error dynamics, and then, a sliding-mode control law is proposed. Low level controller for each vehicle is derived such that it only requires relative position and local motion information of its neighbors in a given directed communication network. The proposed formation control law guarantees the uniform global asymptotic stability (UGAS) of the closed-loop system subject to bounded uncertainties and disturbances. The proposed approach can be applied to underactuated vehicle networks consisting of mobile robots, surface vessels and planar aircraft. Simulations are presented to demonstrate the effectiveness of the proposed control scheme.

A planning framework of environment detection for unmanned ground vehicle in unknown off-road environment

This paper describes a planning framework of environment detection for unmanned ground vehicle (UGV) in the completely unknown off-road environment, which is able to quickly guide the UGV with nonholonomic constraints to detect the environmental information as much as possible. The contributions of this paper contain four fold. First, due to the sensor characteristics of camera and lidar, we present a two-layer combined detection map which can accurately represent the detected and undetected area. Second a frontier extraction algorithm based on RRT considering information acquisition and nonholonomic constraints of UGV is used to extract the target pose. Third, we use a search path planning method based on motion primitive which is able to handle obstacle constraints of environment, nonholonomic constraints of UGV. Fourth the heuristic fusion is proposed to guide the extension of motion primitives to generate a kinodynamically feasible and collision-free trajectory in real-time. And it works well in both simulation and real scene.

Universal Path-Following of Wheeled Mobile Robots: A Closed-Form Bounded Velocity Solution

This paper presents a nonlinear, universal, path-following controller for Wheeled Mobile Robots (WMRs). This approach, unlike previous algorithms, solves the path-following problem for all common categories of holonomic and nonholonomic WMRs, such as omnidirectional, unicycle, car-like, and all steerable wheels. This generality is the consequence of a two-stage solution that tackles separately the platform path-following and wheels’ kinematic constraints. In the first stage, for a mobile platform divested of the wheels’ constraints, we develop a general paradigm of a path-following controller that plans asymptotic paths from the WMR to the desired path and, accordingly, we derive a realization of the presented paradigm. The second stage accounts for the kinematic constraints imposed by the wheels. In this stage, we demonstrate that the designed controller simplifies the otherwise impenetrable wheels’ kinematic and nonholonomic constraints into explicit proportional functions between the velocity of the platform and that of the wheels. This result enables us to derive a closed-form trajectory generation scheme for the asymptotic path that constantly keeps the wheels’ steering and driving velocities within their corresponding, pre-specified bounds. Extensive experimental results on several types of WMRs, along with simulation results for the other types, are provided to demonstrate the performance and the efficacy of the method.

The use of the theory of nonholonomic constraints in the process of automatic control of a manipulating machine

The presented study contains a sample of utilization of the control laws treated as kinematic relations of parameter deviations and realized in the process of ordered automatic control of a manipulating machine. Movement of the grasping end is considered in an inertial reference standard rigidly joined with an immobile working environment of the manipulator. The specificity of the control's choice required creating program relations constituting the ordered parameters describing the movement of the manipulator's elements. During work, the ordered parameters are compared to the parameters realized in the process of the grasping end's work. This was deviations are determined, which thanks to properly prepared control laws are leveled by the manipulator's control executive system.

Two problems of movement of multi-link wheeled vehicles

The paper presents the results of a study of the dynamics of multi-link wheeled vehicles with nonholonomic connections superimposed on this mechanical system. The article is of an overview nature. The mathematical formulation is a system of ordinary differential equations of motion in the form of Lagrange with undefined multipliers, solved together with derivatives of nonholonomic constraints. The results are presented in the case of controlled motion, when the law of motion of the first link is known, as well as in the case of uncontrolled motion, when the law of motion of the leading link is also the desired function of time. General equations are obtained for a mechanical system consisting of an arbitrary number of links. Numerical results are presented for the case of three coupled trolleys. The software package Maple was used to perform numerical calculations and plotting of the desired mechanical parameters.

Modeling and Analysis in Trajectory Tracking Control for Wheeled Mobile Robots with Wheel Skidding and Slipping: Disturbance Rejection Perspective

Wheeled mobile robot (WMR) is usually applicable for executing an operational task around complicated environment; skidding and slipping phenomena unavoidably appear during the motion, which thus can compromise the accomplishment of the task. This paper investigates the trajectory tracking control problem of WMRs via disturbance rejection in the presence of wheel skidding and slipping phenomena. The kinematic and dynamic models with the perturbed nonholonomic constraints are established. The trajectory tracking control scheme at the dynamic level is designed so that the mobile robot system can track the virtual velocity asymptotically, and counteract the perturbation caused by the unknown skidding and slipping of wheels. Both simulation and experimental works are conducted, and the results prove the performance of the proposed control scheme is effective in terms of tracking precision and disturbance attenuation.