基于并联机构的六维加速度传感器的反向动力学

Inverse Dynamics of Six-axis Accelerometers Based on Parallel Mechanisms

六维加速度传感器能够测量完整的空间加速度信息,在人工智能等领域应用前景广阔。由于多输入、多输出量之间的强非线性耦合关系,该类系统的反向动力学问题至今尚未完全解决。以“12-6”、“9-3”两种并联式六维加速度传感器为例,通过引入四元数矩阵和关于四阶向量叉乘的运算规则,在相空间内重新推导并求解了反向动力学方程。据此,揭示了方程数值性态与其影响因素之间的映射规律。研究发现:不计入质量块与基座之间的相对运动参量时,方程的解算效果更优;方程的解算精度主要与弹性体的拓扑构型以及信号频率、采样频率比和采样时间有关;当采样频率小于60 kHz时,方程的解算效率满足实时性要求。结合虚功率原理和特征长度法,求解了两种构型刚度矩阵的最小特征值,找到了弹性体拓扑构型影响方程解算精度的根本原因,这为多维传感器的构型综合提供了理论指导。进一步地,针对方程中存在小扰动和大扰动时解算结果失效的问题,分别通过监测基座的转动方向交替点和构造关于输入量的协调闭链,构建了对应的误差补偿和故障修复算法。实验室条件下,两种构型实物样机的测量误差能够分别控制在5.822%和6.781%之内,且均满足实时性要求,验证了上述反向动力学模型是有效、可靠的。

Six-axis accelerometers can measure the spatial accelerations of moving carriers,which have broad applications in the fields of artificial intelligence and the like.The inverse dynamics of this type of system has not yet been resolved due to the strong nonlinear coupling between multiple inputs and multiple outputs.Taking the six-axis accelerometers based on "12-6" and "9-3" configuration parallel mechanisms as examples,their inverse kinetic equations are derived and solved in the phase space by introducing quaternion matrices and a cross product operation rule related to the fourth-order vectors.Based on these,the relations between the numerical behavior and influencing factors of the equations are revealed.The study found that:the equations are more effective when the relative motion parameters between the mass and the base are ignored;the solution accuracies of the equations are related to the topological configurations of the elastic bodies,the frequencies of the measured signal,the sampling frequency ratios and the sampling time;when the sampling frequencies are less than 60kHz,the solution efficiencies of the equations meet the real-time requirements.Next,the minimum eigenvalues of the stiffness matrices of the two configurations are solved by combining the virtual power principle and the characteristic length method.The root cause of the relations between the elastic body topologies and the accuracies of the equation solutions is found,which provides the theoretical guidance for the configuration synthesis of multi-dimensional sensors.Further,in view of the fact that the accelerations are invalid when there are small or large disturbance in the equations,the corresponding error compensation and fault restoration algorithms are constructed by monitoring the rotation direction alternate point of the base and establishing a compatibility closed chain in terms of the input,respectively.The measurement errors of the physical prototypes of the two configurations can be controlled within 5.822% and 6.781% respectively,both of which meet the real-time request,verifying that the inverse dynamic model is effective and reliable.