3 results about "Axis–angle representation" patented technology

The invention discloses a motion alignment method based on state-dependent Bayesian group filtering, which is used for solving the problems of rapid attitude change and state-dependent noise in high-dynamic initial alignment of a strapdown inertial navigation system. The method has two creative points. The method comprises the following steps: firstly, establishing an accurate initial alignment model containing an inertial sensor error by utilizing Lie group representation; an observation probability model is established by adopting a shaft angle model which is more in line with physical definition, and the rotation of the carrier is described and tracked more accurately. Secondly, in the process of designing a state correlation Lie group Bayesian filtering algorithm, exact composition of state correlation noise in the alignment model is deduced and analyzed, and observation noise and the state are decoupled through vector dot product and cross product; experimental results show that the method is obviously superior to the existing method in alignment precision and time.

The present invention discloses a high-efficiency and stable method for simulating inextensible ropes in crane and hoist. The piecewise linear inextensible rope is usually represented by the Cartesian coordinates of the vertices and the quaternions on the segments, which uses too many degrees of freedom and needs many constraints, bringing unnecessary numerical difficulties and computational burden to the simulation. The present invention proposes a compact representation which uses the minimum number of degrees of freedom and naturally satisfies all the additional constraints. Specifically, the rope is regarded as a chain of rigid segments, and its shape is encoded as the Cartesian coordinates of its root vertex and the axis-angle representation of the local coordinate system on each segment. Under the representation of the present invention, the implicit time-stepping matrix has a special non-zero pattern. Using the non-zero pattern, the present invention designs a preconditioner which can solve the related linear equations with approximate linear complexity, and its speed is improved by one to two orders of magnitude compared with the widely used block-diagonal linear PCG solver.

The application discloses an impedance control method and device based on an axis angle representation, equipment and a storage medium. A Jacobian matrix of a rotation angle and a three-dimensional direction vector with respect to a joint angle and a matrix irrelevant to a joint angular velocity in a second-order derivative of a product of the rotation angle and the three-dimensional direction vector with respect to time are calculated according to the rotation angle and the three-dimensional direction vector. A mathematical relationship of a robot joint instruction torque is constructed according to a robot Jacobian matrix, the Jacobian matrix of the rotation angle and the three-dimensional direction vector with respect to the joint angle, the matrix irrelevant to the joint angular velocity in the second-order derivative of the product of the rotation angle and the three-dimensional direction vector with respect to time, the rotation angle and the three-dimensional direction vector. The robot joint instruction torque is obtained by solving the mathematical relationship of the robot joint instruction torque according to a preset constraint function. The application aims to eliminate nonlinear factors of a dynamic relationship in impedance control.