A New Methodology for Inverse Kinematics and Trajectory Planning of Humanoid Biped Robots
Rodríguez Said, Alejandro
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This dissertation presents a new methodology for Inverse Kinematics and Trajectory Planning for small-sized humanoid biped robots. Regarding the Inverse Kinematics, this study presents an explicit, omnidirectional, analytical, and decoupled closed-form solution for the lower limb kinematics of the humanoid robot NAO. It starts by decoupling the position and orientation analysis from the concatenation of Denavit-Hartenberg (DH) transformation ma- trices. Here, the joint activation sequence for the DH matrices is mathematically constrained to follow the geometry of a triangle. Furthermore, the implementation of a forward and a reversed kinematic analysis for the support and swing phase equations is developed to avoid the complexity of matrix inversion. The allocation of constant transformations allows the position and orientation end-coordinate systems to be aligned with each other. Also, the re- definition of the DH transformations and the use of constraints allows for the decoupling the shared Degree of Freedom (DOF) located between the legs and the torso; and which activates the torso and both of the legs when a single actuator (the hip-yaw joint) is activated. Further- more, a three dimensional geometric analysis is carried out to avoid the singularities during the walking process. Numerical data is presented along with experimental implementations to prove the validity of the analytical results. In relation to the trajectory planning, a method taken from manipulator robot theory is applied to humanoid walking. Fifth and seventh order polynomials are proposed to define the trajectories of the Center of Gravity (CoG) and the swing foot. The polynomials are designed so that the acceleration and jerk are constrained to be zero particularly at two moments: at the single support phase (when the robot is standing on a single foot), and at the foot landing (to prevent foot-to-ground impacts); thus, minimizing internal disturbance forces. Computer simulations are performed to compare the effects of the acceleration and jerk constraints. In addition, the basics of the future work is given by providing a control model for robot equilibrium. First, the analysis of this model starts with a static equilibrium model which reacts to an ankle perturbation by using a hip actuation. Second, a dynamic model is proposed which incorporates the ground perturbations into the robot model by representing the ground tilt as an additional, passive, and redundant DOF located at the ankle. This procedure allows for two separate models (the one corresponding to the humanoid and the one corresponding to the ground) to be accounted into a single model, thus, minimizing complexity.
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