Hierarchical quadratic programming: Fast online humanoid-robot motion generation

Abstract

International audienceHierarchical least-square optimization is often used in robotics to inverse a direct function when multiple incompatible objectives are involved. Typical examples are inverse kinematics or dynamics. The objectives can be given as equalities to be satisfied (e.g. point-to-point task) or as areas of satisfaction (e.g. the joint range). This two-part paper proposes a complete solution to resolve multiple least-square quadratic problems of both equality and inequality constraints ordered into a strict hierarchy. Our method is able to solve a hierarchy of only equalities ten time faster than the classical method and can consider inequalities at any level while running at the typical control frequency on whole-body size problems. This generic solver is used to resolve the redundancy of humanoid robots while generating complex movements in constrained environment. In the first part, we establish the mathematical bases underlying the hierarchical problem and propose a dedicated solver. When only equalities are involved, the solver amounts to the classical solution used to handle redundancy in inverse kinematics in a far more efficient way. It is able to handle inequalities at any priority levels into a single resolution scheme, which avoids the high number of iterations encountered with cascades of solvers. A simple example is given to illustrate the interest of our approach. In the second part, we detail the implementation of the solver and its application to inverse kinematics. In particular, we explicit the solver complexity and prove the continuity and the stability of the resulting control laws. Finally, we experimentally demonstrate its efficiency in the context of generating robot motions

The Next Step in Robot Commissioning: Autonomous Picking and Palletizing

“…We lean on the notation in [26] and describe the manipulator joint configuration with the vector q and the control inputs as corresponding joint velocitiesq. A task function e(q) is any derivable function of q.…”

“…As stated in [26], this allows to transcribe lower bounds Jq ≥ė * , double boundsė * ≤ Jq ≤ė * and equalities Jq =ė * by reformulating the task respectively as To form a hierarchical SoT with p = 1, . .…”

“…Regarding the manipulator, we use a joint impedance controller to track the reference velocities obtained in each time step by solving (4). If a sufficiently accurate dynamic model were available, the scheme could easily be adapted to torque control [26]. However, we are not considering this option at present.…”

Multi-contact haptic exploration and grasping with tactile sensors

“…Recently, hierarchical control schemes based on a sequence of quadratic programs (QP) can also handle inequality constraints for kinematic control [21] and dynamic control [22]. Efforts have also been made to solve these problems fast enough for real-time control of humanoid robots with many degrees of freedom [23].…”

Modeling Robot Geometries Like Molecules, Application to Fast Multicontact Posture Planning for Humanoids

“…One popular approach is to find a time evolution of internal coordinates that converges to the optimal posture. This can be done via inverse kinematics (IK) [3] or inverse-dynamics (ID) formulations [1], [4] which offer compliance as well. In these time-integration controllers, an optimal posture is found naturally, but with certain dynamics.…”