Gait and balance kinematic control for a humanoid robot based on dual quaternion algebra

Abstract

In this work, we present a novel method to obtain the kinematic model for a humanoid robot based on dual quaternion (DQ) algebra, and propose a control strategy that fulfills the kinematic constraints for a balanced gait. The modeling method consists of three stages: the robot's limbs modeling, the center of mass modeling, and the legs cooperative behavior modeling using the Cooperative Dual Task-Space Framework. The advantages of the novel modeling method are its compactness and lower computational effort required to calculate the model, when compared with methods based on homogeneous transformation matrices (HTMs), since DQs has only eight parameters whereas HTMs has twelve, and also because DQs multiplications are less expensive than HTMs multiplications. In addition, its coefficients can be directly used in a control law, differently from HTMs. The presented control strategy was designed using the pseudo-inverse of a Jacobian matrix representing the locomotion task with a velocity feed-forward term, and an additional task, designed to keep the arms close to the desired configuration, was included in the null space of this Jacobian matrix. We validated the obtained model and the proposed controller using the virtual reality simulation software for robotic systems V-REP. The data estimated using the model and the measured values were very close, showing that the modeling method is accurate and provides reliable information. Furthermore, the robot successfully performed different walking motions when controlled by the proposed strategy, and was capable of keeping the balance even when the arms were moving. This work is the first stage of the Popeye Project, whose goal is to build a test framework for a real humanoid robot. As future works, we intend to implement the proposed methods in a real robot; to reduce the time response of the joints controllers by adjusting their gains; to enhance the control strategy to guarantee disturbances rejection; and to implement the methods in a programming language that guarantees a lower latency time.