Trabajo de grado, Doctorado / doctoral Degree Work
A New Methodology for Inverse Kinematics and Trajectory Planning of Humanoid Biped Robots
Registro en:
Rodriguez, A., (2019). A New Methodology for Inverse Kinematics and Trajectory Planning of Humanoid Biped Robots (Tesis doctoral). Tecnologico de Monterrey, Monterrey N.L., México
Autor
0000-0003-4925-5189
Rodríguez Said, Alejandro
Institución
Resumen
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.