C2-Continuous Orientation Planning for Robot End-Effector with B-Spline Curve Based on Logarithmic Quaternion

Smooth orientation planning is beneficial for the working performance and service life of industrial robots, keeping robots from violent impacts and shocks caused by discontinuous orientation planning. Nevertheless, the popular used quaternion interpolations can hardly guarantee C2 continuity for multiorientation interpolation. Aiming at the problem, an efficient quaternion interpolation methodology based on logarithmic quaternion was proposed. Quaternions of more than two key orientations were expressed in the exponential forms of quaternion. These four-dimensional quaternions in space S3, when logarithms were taken for them, could be converted to three-dimensional points in space R3 so that B-spline interpolation could be applied freely to interpolate. The core formulas that B-spline interpolated points were mapped to quaternion were founded since B-spline interpolated point vectors were decomposed to the product of unitized forms and exponents were taken for them. The proposed methodology made B-spline curve applicable to quaternion interpolation through dimension reduction and the high-order continuity of the B-spline curve remained when B-spline interpolated points were mapped to quaternions. The function for reversely finding control points of B-spline curve with zero curvature at endpoints was derived, which helped interpolation curve become smoother and sleeker. The validity and rationality of the principle were verified by the study case. For comparison, the study case was also analyzed by the popular quaternion interpolations, Spherical Linear Interpolation (SLERP) and Spherical and Quadrangle (SQUAD). The comparison results demonstrated the proposed methodology had higher smoothness than SLERP and SQUAD and thus would provide better protection for robot end-effector from violent impacts led by unreasonable multiorientation interpolation. It should be noted that the proposed methodology can be extended to multiorientation quaternion interpolation with higher continuity than the second order.

Research on Attitude Interpolation and Tracking Control Based on Improved Orientation Vector SLERP Method

SummaryIn order to make the end of the three-axis platform follow the control command and achieve stable control of the end attitude, an improved orientation vector spherical linear interpolation (SLERP) method is proposed for the requirements, which specifically handles the position of the gimbal lock, so that the platform can move smoothly around the gimbal lock position. A three-axis platform with a camera at the end is set up for the validity of the proposed algorithm. At first, an adaptive speed measurement method based on incremental encoder is introduced, which can automatically adapt to high and low speed, and estimate the ultra-low speed to realize the speed measurement of large dynamic range, and this is used for the motion control of the three-axis platform. Then, the SLERP method for the quaternion interpolation on the starting and ending attitudes represented in quaternion is introduced in detail, and it is continuously improved in response to its existing problems for the platform. Finally, an orientation vector SLERP method is proposed, which uses viscosity factor and rejection factor to adjust the algorithm near the platform’s gimbal lock position. A tracking experiment was designed using the red ball as the following target detected by the designed target tracking algorithm using the camera, which verified the effectiveness of the attitude tracking control based on the proposed improved orientation vector SLERP.

IMU Signal Generator Based on Dual Quaternion Interpolation for Integration Simulation

This paper focuses on the problem of high-update-rate and high accuracy inertial measurement unit signal generation. In order to be in accordance with the vehicle’s kinematic and dynamic characteristics as well as the characteristics of pseudorange of post-processed global navigation satellite system and their rate measurements, a novel dual quaternion interpolation and analytic integration algorithm based on actual flight data is proposed. The proposed method can simplify the piecewise analytical expressions of angular rates, angular increments and specific force integral increments. Norm corrections are adopted as constraint conditions to guarantee the accuracy of the signals. Numerical simulations are conducted to validate the method’s performance.

C2-continuous orientation trajectory planning for robot based on spline quaternion curve

Purpose To realize the smooth interpolation of orientation on robot end-effector, this paper aims to propose a novel algorithm based on the unit quaternion spline curve. Design/methodology/approach This algorithm combines the spherical linear quaternion interpolation and the cubic B-spline quaternion curve. With this method, a C2-continuous smooth trajectory of multiple teaching orientations is obtained. To achieve the visualization of quaternion curves on a unit sphere, a mapping algorithm between a unit quaternion and a point on the spherical surface is given based on the physical meaning of the unit quaternion. Findings Finally, the curvature analysis of a practical case shows that the orientation trajectory (OT) constructed by this algorithm satisfied the C2-continuity. Originality/value This OT satisfies the requirement of smooth interpolation among multiple orientations on robots in industrial applications.

Application of Automatic Choreography Software Based on Virtual Technology in the Gymnastics Teaching

this research designed simulation system of gymnastics automatic choreography software. To successfully design the gymnastics movements, experiment adopted solutions based on key frame spline interpolation calculation which managed to solve the problem of location deviation; quaternion interpolation algorithm was adopted to solve the rotation problem of the subject and the body, which made the modified action by computer auxiliary choreography system completely returned to virtual figure animation. In addition, for coordination of dance and audio, this paper established movement fragments library based on sentiment types, proposed viable approach of synchronized audio and video model. Teaching experience was conducted in the gymnastics course of physical education at the University and achieved good results.