![]() The proposed solution was made feasible through a decomposition into five independent problems (head, two arms, two legs), the use of the Denavit-Hartenberg method, the analytical solution of a non-linear system of equations, and the exploitation of body and joint symmetries. ![]() The forward kinematics allow NAO developers to map any configuration of the robot from its own joint space to the three-dimensional physical space, whereas the inverse kinematics provide closed-form solutions to finding joint configurations that drive the end effectors of the robot to desired target positions in the three-dimensional physical space. In this paper, we study the problems of forward and inverse kinematics for the Aldebaran NAO humanoid robot and present a complete, exact, analytical solution to both problems, including a software library implementation for real-time on-board execution. The design of complex dynamic motions for humanoid robots is achievable only through the use of robot kinematics. With the proposed algorithm, the apple harvesting success rate of a lab-customized 11-DOFs robot reaches 89.2%, which can be further increased up to 93.3% with error compensation, while the average time starting from the robot action to the end-effector reaching the target pose of the apple is around 12.3 s. Such results indicate that the proposed mechanism is reliable and capable of reducing the complexity of IK for multi-DOFs humanoid robots. Results show that the errors in position and orientation are less than 0.005 mm and 0.007°, respectively, and the average computational time is less than 2 s for the IK solution of the entire robot. Under the various scenarios with different target and obstacle configurations, errors in position coordinates and orientation angles between the target pose and those of the end-effector obtained with forward kinematics (FK) are calculated. The proposed TDM based mechanism is verified via experiments using a lab-customized humanoid apple harvesting robot with 11- and 13-DOFs, respectively. Furthermore, a Reverse & Random Rotation (RRR) algorithm is also proposed to solve the IK of the upper part subsystem in unstructured environments, while the IK of the lower part subsystem is solved analytically. Specifically, the division point is selected such that the lower part subsystem has 6-DOFs, while the upper part subsystem has (n-6)-DOFs. Once a collision-free configuration is found for the upper part subsystem to match with the target, the lower part subsystem is then planned to merge with the upper part subsystem at the division point. For any robot with n-DOFs (n>6), a division point is selected first to divide it into a lower part subsystem from its base to the division point, together with an upper part one from the point to its end-effector. Moreover, because only one parameter needs to be adjusted when applying the balance-control system, the system can be easily extended to any related humanoid robot.Ī Two-step Division-Merge (TDM) based inverse kinematics (IK) mechanism is proposed for robots with multiple degrees of freedom (multi-DOFs) in unstructured environments. A robot with an open platform was used to test the implementation of the proposed algorithm, and the experimental results demonstrated that the robot could successfully maintain balance when walking uphill and downhill on uneven surfaces. The system further modifies the gait and posture of the robot based on the results obtained through a fuzzy system to attain the angle of balance and stabilization. To process the data obtained by the sensors, the mean filter was applied to eliminate the noise in the data, and the complementary filter was used to properly combine the data from both the gyroscope and accelerometer. In this study, we first examined the problem of gait generation and the balance of a humanoid robot and then proposed a posture-control balance system using the inertial sensors of a gyroscope and accelerometer to sense the tilt angle of the robot according to the environment. We designed a stable gait pattern and posture-control balance system to enable a biped humanoid robot to maintain balance and avoid falling when walking on uneven ground or slopes.
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