Extended Kinematic Model Research Articles

A comprehensive error evaluation method for non-rigid body gantry machine tools considering quasi-static crosstalk based on optimized multilateration measurement

For large-scale machine tools, the impact of non-rigid body behavior on volumetric error accuracy cannot be ignored, which hasn't been considered in general volumetric error model. This paper presents a comprehensive error evaluation method for large-scale gantry machine tools considering non-rigid body effect, aiming to provide guidance for volumetric error calibration process. An extended kinematic model is established based on the analysis of crosstalk influence on geometric error motions. An optimized multilateration measurement with improved accuracy and robustness is carried out for volumetric error identification, verified by Monte Carlo simulations. The main novelty of the optimization is to introduce a space uniformity index to generate specialized calibration point sets for any measurement points. A new volumetric error prediction method based on classified descriptions of geometric error motions is proposed, according to their relationship with crosstalk. Experimental results show that the proposed method achieves higher prediction accuracy in crosstalk-sensitive directions.

Motion control for a differential vehicle with variable point of interest. Application: Smart cane control

This article addresses an unified solution to the trajectory tracking and path following problems for differential drive mobile robots (DDMR) considering a point of interest (PoI) with variable location relative to the vehicle. The mobile robot is modeled with an extended kinematic model avoiding typical singularities of this kind of vehicles, and allowing a straightforward definition of the corresponding inverse kinematics controller (IKC). This classical IKC fulfills the control objective with exponential error convergence but with the shortcoming of generating backward navigation when the PoI is located behind the DDMR, which is undesirable in some practical applications where the forward navigation must be preserved. This situation is theoretically analyzed, concluding that even though both forward and backward navigations correspond to equilibrium points of the closed loop, the stability of the forward navigation requires a PoI located in front of the DDMR, and the stability of the backward navigation requires a PoI located behind the DDMR. Finally, the article presents novel alternative controllers in order to always fulfill the motion objectives with stable forward navigation. Simulation results are presented to show the performance of the proposed controllers, and a real application of a robotic cane guiding its user is experimentally developed.

Robust sideslip angles observer for accurate off-road path tracking control

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Dynamic path tracking control of a vehicle on slippery terrain

This paper deals with accuracy and reliability for the path tracking control of a four wheel mobile robot with a double-steering system when moving at high dynamics on a slippery surface. An extended kinematic model of the robot is developed considering the effects of wheel–ground skidding. This bicycle type model is augmented to form a dynamic model that considers an actuation of the four wheels. Based on the extended kinematic model, an adaptive and predictive controller for the path tracking is developed to drive the wheels front and rear steering angles. The resulting control law is combined with a stabilization algorithm of the yaw motion which modulates the actuation torque of each four wheels, on the basis of the robot dynamic model. The global control architecture is experimentally evaluated on a wet grass slippery terrain, with speeds up to 7m/s. Experimental results demonstrate enhancement of tracking performances in terms of stability and accuracy relative to the kinematic control.

Trajectory Tracking for a Group of Unicycle-type Robots using an Attitude Observer

The trajectory tracking problem for a group of unicycle-type robots is addressed and solved by means of a partial state feedback strategy based on the leader-followers scheme using an observer to estimate the orientation angle of each mobile robot. The control law is based on an extended kinematic model where the output function to be controlled is the mid-point of the wheels axis of each robot. This choice leads to an ill defined control law when the robot is at rest. To avoid such a singularity, a complementary control law is enabled when the linear velocity of each robot is close to zero. It is shown that the combination of a classical dynamic full information controller with an exponentially convergent vehicle attitude observer yields an asymptotically stable closed-loop system. Real-time experiments show the performance of the proposed control scheme.

Adaptive and Predictive Path Tracking Control for Off-road Mobile Robots

A major problem in the design of control laws dedicated to mobile robots appears when the classical hypothesis of rolling without sliding wheels is violated. It is generally the case for off-road vehicles as adherence conditions are often not satisfactory and sliding can then cease to be negligible. Consequently theoretical performance is impaired and the vehicle is no longer accurately controlled. It is particularly harmful with respect to path tracking tasks, where a loss of accuracy in rough terrain can generate a hazardous situation. Previous work based on the assumption of rolling without sliding has shown very satisfactory results with respect to that task when sliding is not preponderant. It has also made it possible to pinpoint and study the effects of sliding when it appears to be non-negligible. To preserve path tracking accuracy with respect to this phenomenon, a new control law based on an extended kinematic model (updated on-line via an adaptive method) is proposed and discussed. Such control is very efficient when adherence conditions are constant, but overshoots can appear when an abrupt variation is recorded (which is especially the case at the beginning/ end of curves due to low level delays and inertial effects). A model predictive control approach is then added to limit such transient phases in cases where a curved path is followed. The paper is organized as follows: the extended kinematic model is presented as well as the observation of unmeasured parameters required to feed it. A nonlinear control law can then be designed and the results obtained are discussed. Finally, the model predictive control approach is integrated and the overall control scheme is presented. The capabilities of the approach described in this paper are then discussed through full scale experiments.

Internal singularity analysis of a class of lower mobility parallel manipulators with articulated traveling plate

This paper deals with a particular family of lower mobility parallel kinematic manipulators. The four degrees of freedom of the end-effector consist of three translations plus one rotation with a high tilting angle. Robots belonging to this family are first introduced, and a common parameterization is established. Then an extended kinematic model is proposed for this family of robots using a new Jacobian matrix. Relevant information about robot kinematic singularities, internal singularities, and possible end-effector motions can be obtained by resorting to this matrix. The efficiency of this method is proven by applying it to several traveling-plate architectures corresponding to already built robot prototypes. The results of the expected behavior are compared with the prototype's real behavior. The goal of this paper is to show that internal (or constraint) singularities can occur in lower mobility parallel kinematic manipulators, and to underline the influence they have during the design stage.