The product of exponential model based robot calibration approach eliminates parameter discontinuity and simplifies coordinate frame setup, but demands extra effort to normalize twist coordinates and differentiate parameter-varying exponential maps. In this paper, we show that such an endeavor can be exempted by respecting the nonlinear geometry of the joint axis configuration space (ACS), the set of all possible axis locations. We analyze the geometry of the ACS models for prismatic and revolute joints, and treat the errors as Adjoint transformations on joint twists. We propose a novel robot kinematic calibration algorithm based on the ACS and Adjoint error model. It is geometrically intuitive, computationally efficient, and can easily handle additional assumptions on joint axes relations. We present a comparative study with simulations and experiments to show that our algorithm outperforms the existing ones in various aspects.

This paper presents a novel quadrotor UAV attitude control algorithm to realize complex acrobatic UAV maneuvers. A nonlinear dynamic model based on the exponential coordinates parametrization of rotation is proposed. By analysing the model using Lie Group and Lie Algebra theory, cascaded linear PID controllers are designed. To further improve the controller performance, PID controllers are augmented with smith predictor and rotational trajectory planner. The experiments conducted on a real quadrotor show that our control algorithm surpasses most known quadrotor controllers.

In this paper, we first analyze the identifiability of POE based Adjoint error approach. By carefully examining the linear dependence between calibration Jacobian columns, it is proved that joint offsets and Adjoint errors cannot be identified simultaneously, and the maximum dimension of identifiable parameters is 4r + 2t + 6. Some more scenarios are considered to augment the Adjoint error approach. To satisfy the constraints on joint relations, constrained method and projection method are proposed. Moreover, we present the identifiability of reduction ratios and joint pitches. Simulations of a 6 Degree-of-Freedom robot and a SCARA robot are given to illustrate and compare our methods. It shows that the constrained method can handle such situations effectively and yields better results.

In this paper, we conduct a comparative study of three well known robot kinematic calibration algorithms, namely the Denavit-Hartenberg (DH) parameter algorithm, the product of exponentials (POE) algorithm, and the local POE (LPOE) algorithm. To cope with distinct formulations associated to different algorithms, we propose a unified geometric framework which is based on POE kinematics and a novel Adjoint error model. The Adjoint error model offers us an extremely efficient way to benchmark the aforesaid calibration algorithms, and also compare them to a novel calibration algorithm based on the Adjoint error model.

In this paper, we present an experimental evaluation of the Cartesian stiffness of a novel parallel wrist under redundant and antagonistic actuation. The mechanism in consideration is Omni-Wrist V (OW5), a two degrees-of-freedom (DoF) parallel mechanism redundantly actuated by three subchains. We first give a brief review of its kineto-statics and derive its reduced Cartesian stiffness model. To illustrate the stiffness enhancement of OW5 under redundant and antagonistic actuation, its Cartesian stiffness is measured and evaluated under four control schemes: the non-redundant control, the minimum 2-norm torque control without or with redundant encoder, and the antagonistic actuation control. Measurement data are represented using stiffness matrices and stiffness ellipses. Our study offers a quick quantitative evaluation of stiffness enhancement of OW5 under redundant and antagonistic actuation.