In this paper, a Lie coordinate-free torque based Euler–Lagrange equations of motion are developed for a 3-D link (3-DOF) robot. Intentional torque and jerky torque (non-intentional torque) are considered as the inputs to the dynamic profile of the robot. The jerky torque is modelled as a superposition of compound Poisson processes, which is a unique feature. The state vector of the robot, i.e., angular position and angular velocity vector, is thus a Markov process whose transition probability generator can be expressed in terms of the rate of the compound Poisson process that defines the jerky torque. Proof of frame invariance is provided to support the coordinate-free robot dynamics profile. Noise-free measurement is investigated as an ideal case. Angular position measurement is considered with white Gaussian noise. Further, an implementable finite-dimensional EKF approximate to Kushner–Kallianpur filter is obtained to estimate the robot state vector. Finally, the simulations are implemented on commercially available Omni bundle robot.

在本文中，为3-D链接（3-DOF）机器人开发了基于Lie无坐标的转矩的Euler-Lagrange运动方程。故意转矩和抖动转矩（非故意转矩）被视为机器人动态曲线的输入。颠簸转矩被建模为复合泊松过程的叠加，这是一个独特的功能。因此，机器人的状态向量（即角位置和角速度向量）是马尔可夫过程，其转移概率生成器可以根据定义了抖动转矩的复合泊松过程的速率来表示。提供帧不变性证明以支持无坐标机器人动态特性文件。研究无噪声测量是一种理想情况。角度位置测量被考虑为高斯白噪声。进一步，获得了近似于库什纳-卡利安布尔滤波器的可实现的有限维EKF，以估计机器人状态向量。最后，仿真是在市售的Omni捆绑机器人上实现的。