Shaoping Bai

A new free gait generation for quadrupeds based on primary/secondary gait

A method of free gait generation for quadrupeds is presented by introducing the primary/secondary gait. The primary gait is a fixed sequence of leg transfers with modified leg-ends kinematic limits according to the obstacle presence, while the secondary gait is a flexible gait which is generated to adjust the leg-end position. Using the proposed method, a machine tends to move with primary gait during the motion. When the primary gait cannot move the vehicle, the secondary gait is adopted to serve as a complement of the primary gait. Four constraints, namely, stability constraint, kinematic constraint, sequential constraint and neighboring constraint are considered when gaits are generated. The influence of the obstacle is taken into account to modify the gait parameters. With the proposed method based on primary/secondary gait, it is expected to improve the efficiency of free gait generation while maintaining the mobility of the vehicle. Simulation results are given to demonstrate the efficiency of the proposed algorithm.

Kinematic Calibration and Pose Measurement of a Medical Parallel Manipulator by Optical Position Sensors

In the applications of parallel manipulators, kinematic calibration is required to eliminate the errors resulting from the manufacturing and assembly of both base and tools. In this paper, a calibration method of base and tool transformation is developed by virtue of optical position sensors. An error model for calibration is constructed using differential geometry method. The pose error is obtained based on pose measurement results of OPTOTRAK 3020, a commercial 3D position measurement system. An iterative least squares procedure is used to identify the error parameters in the base and tool transformations. Simulation and experiment results are presented to demonstrate the effectiveness of the method for transformation matrices calibration.

Modelling of a special class of spherical parallel manipulators with euler parameters

A method of workspace modelling for spherical parallel manipulators (SPMs) of symmetrical architecture is developed by virtue of Euler parameters in the paper. The adoption of Euler parameters in the expression of spatial rotations of SPMs helps not only to eliminate the possible singularity in the rotation matrix, but also to formulate all equations in polynomials, which are more easily manipulated. Moreover, a homogeneous workspace can be obtained with Euler parameters for the SPMs, which facilitates the evaluation of dexterity. In this work, the problem of workspace modelling and analysis is formulated in terms of Euler parameters. An equation dealing with boundary surfaces is derived and branches of boundary surface are identified. Evaluation of dexterity is explored to quantitatively describe the capability of a manipulator to attain orientations. The singularity identification is also addressed. Examples are included to demonstrate the application of the proposed method.

Dynamic modeling and design optimization of a 3-DOF spherical parallel manipulator

This paper deals with the dynamic modeling and design optimization of a three Degree-of-Freedom spherical parallel manipulator. Using the method of Lagrange multipliers, the equations of motion of the manipulator are derived by considering its motion characteristics, namely, all the components rotating about the center of rotation. Using the derived dynamic model, a multiobjective optimization problem is formulated to optimize the structural and geometric parameters of the spherical parallel manipulator. The proposed approach is illustrated with the design optimization of an unlimited-roll spherical parallel manipulator with a main objective to minimize the mechanism mass in order to enhance both kinematic and dynamic performances.

Quadruped Free Gait Generation Based on the Primary/Secondary Gait

A free gait algorithm is proposed utilizing a new method of gait generation called primary/secondary gait. The primary gait is a fixed sequence of leg transfers with modified leg-end kinematic limits according to the obstacle presence, while the secondary gait is a flexible gait which is generated to adjust the leg-end position. The primary gait is generated considering the following four constraints: stability constraint, kinematic constraint, sequential constraint and neighboring constraints. Primary gait parameters are modified by the influence of the obstacle. Normally, the machine tends to move with the primary gait. When the primary gait cannot move the vehicle, the secondary gait is adopted to serve as a complement of the primary gait. With the proposed primary/secondary gait, it is expected to improve the efficiency of free gait generation while maintaining the mobility of the vehicle. Simulation results are given to demonstrate the efficiency of the proposed methodology.

Error Modeling and Experimental Validation of a Planar 3-PPR Parallel Manipulator With Joint Clearances

This paper deals with the error modelling and analysis of a 3-\underline{P}PR planar parallel manipulator with joint clearances. The kinematics and the Cartesian workspace of the manipulator are analyzed. An error model is established with considerations of both configuration errors and joint clearances. Using this model, the upper bounds and distributions of the pose errors for this manipulator are established. The results are compared with experimental measurements and show the effectiveness of the error prediction model.

Quadruped free gait generation for straight-line and circular trajectories

A method of free gait generation is proposed utilizing the primary/secondary gait for both straight line and circular body trajectories. The primary gait is a fixed sequence of leg transfers with modified leg-ends kinematic limits according to the presence of obstacles, while the secondary gait is a flexible gait which is generated to adjust the leg-end position. The primary gait is generated considering the following four constraints: stability constraint, kinematic constraint, sequential constraint and neighboring constraints. A generalized reference coordinate (GRC) system is introduced to describe the vehicle motion. Using the GRC system, all constraints and obstacle influences are expressed by only one set of equations despite the difference of motion mode. The efficiency of free gait generation is improved with the proposed method, and the trajectory of the vehicle body can be designed more naturally. Simulation results are given to demonstrate the efficiency of the proposed methodology.

Terrain evaluation and its application to path planning for walking machines

Motion planning of walking machines normally contains two aspects: gait planning and body trajectory planning. When generating an optimal body trajectory on natural terrain, the leg movement must be taken into account. Due to the large searching space resulting from the combination of leg movement and terrain conditions, it is quite time consuming to produce an optimal result of body trajectory planning. In this paper, an effective method of body trajectory planning is introduced by virtue of a terrain evaluation that links the terrain conditions with machine mobility. Based on the evaluation, a potential field is constructed for graph searching. Best first planning (BFP) is adopted to search the optimal path. The path generated with the proposed method could offer the best opportunity to place the machine feet moving with a certain gait over a rough terrain. The assumptions and shortages associated with the present work are also discussed.

Path generation of walking machines in 3D terrain

The path planning of legged locomotion is difficult in that not only the body trajectory but also the foot placement need to be considered. A general approach of path planning will fail in generating a feasible path for walking machines when facing the huge searching space of legged locomotion. In this paper, an effective method of path planning for 3D walking is introduced. The basic idea is that a feasible path is generated based on the terrain evaluation which produces an index of terrain complexity with respect to the machine mobility. The terrain evaluation is first carried out in a 2D space by considering the leg placement. The 2D terrain complexity is then modified according to the heights influence on the body motion for the 3D results. As an illustration, a feasible path is generated by applying the potential-guided searching technology to the 3D terrain complexity.

The Design of a Chain of Spherical Stephenson Mechanisms for a Gearless Robotic Pitch-Roll Wrist

Although bevel-gear robotic wrists are widely used in industrial manipulators due to their simple kinematics and low manufacturing cost, their gear trains function under rolling and sliding, the latter bringing about noise and vibration. Sliding is inherent to the straight teeth of the bevel gears of these trains. Moreover, unavoidable backlash introduces unmodeled dynamics, which mars robot performance. To alleviate these drawbacks, a gearless pitch-roll wrist is currently under development for low backlash and high stiffness. The wrist consists of spherical cam-rollers and spherical Stephenson linkages, besides two roller-carrying disks that drive a combination of cams and Stephenson mechanisms, the whole system rotating as a differential mechanism. The paper focuses on the design of the chain of spherical Stephenson mechanisms. The problem of the dimensional synthesis is addressed, and interference avoidance is discussed. An embodiment of the concept is also included.