Abstract-The most widely-used technique to generate wholebody motions on a humanoid robot accounting for various tasks and constraints is the inverse kinematics. Based on the taskfunction approach, this class of methods makes possible the coordination of the robot movements to execute several tasks in parallel and account for the sensor feedback, in real-time thanks to the low computation cost. To some extent, it also enables dealing with some of the robot constraints (e.g. joint limits or visibility) and managing the quasi-static balance of the robot. In order to fully use the whole range of possible motions, this paper proposes to extend the task-function approach to handle the full dynamics of the robot multi-body along with any constraint written as equality or inequality of the state and control variables. The definition of multiple objectives is made possible by ordering them inside a strict hierarchy. Several models of contact with the environment can be implemented in the framework. We propose a reduced formulation of the multiple rigid planar contact that keeps a low computation cost. The efficiency of this approach is illustrated by presenting several multi-contact dynamic motions in simulation and on the real HRP-2 robot.

In this paper, we propose a solution to compute full-dynamic motions for a humanoid robot, accounting for various kinds of constraints such as dynamic balance or joint limits. As a first step, we propose a unification of task-based control schemes, in inverse kinematics or inverse dynamics. Based on this unification, we generalize the cascade of quadratic programs that were developed for inverse kinematics only. Then, we apply the solution to generate, in simulation, wholebody motions for a humanoid robot in unilateral contact with the ground, while ensuring the dynamic balance on a non horizontal surface.

In October 2012, the humanoid robot HRP-2 was presented during a live demonstration performing finebalanced dance movements with a human performer in front of more than 1000 people. This success was possible by the systematic use of operational-space inverse dynamics to compute dynamically consistent movements following a motion capture pattern demonstrated by a human choreographer. The first goal of this article is to give an overview of the efficient inverse-dynamics method used to generate the dance motion. Behind the methodological description, the second and main goal of the article is to present the robot dance as the first successful real-size implementation of inverse dynamics for humanoid-robot movement generation. This gives a proof of concept of the interest of inverse dynamics, which is more expressive than inverse kinematics and more computationally tractable than model-predictive control. It is, in our opinion, the topical method of choice for humanoid whole-body movement generation. The real-size demonstration also gave us some insight of nowadays methodological limits and the consequent future needed developments. 1 With this representation equalities are a special case when b i = b i and single-sided inequalities are special cases when b i = −∞ or b i = +∞.