Humanoid Locomotion Control and Generation Based on Contact Wrench Cones

This paper presents a general framework for locomotion control and generation of humanoid robots. Different from most of the existing work which uses the zero-moment point (2mp) to determine the feasibility of robot’s motion, we use the so-called contact wrench cone to derive motion feasibility conditions, whole-body motion controllers, and locomotion generators. The contact wrench cone consists of all feasible wrenches that can be applied to the robot through contacts, which provide allowable external forces and moments for realizing the robot’s motion. Algorithms are proposed to compute quantities defined on linear representations of a general convex cone, which can be various contact wrench cones as needed in developing motion generators and controllers. Based on the contact wrench cone for contact links and the proposed algorithms as well as a decomposition of the whole-body dynamics of a floating-base humanoid robot, we derive two motion tracking controllers. One controller contains a single quadratic program with linear inequality constraints, while the other consists of two quadratic programs which can be quickly solved by one of the proposed algorithms and in a closed form, respectively. Both controllers can be applied in real-time and achieve similar motion tracking performance in simulation. Based on contact wrench cones, furthermore, we derive two motion generation methods for humanoid robots. The first method adapts a reference motion, most often infeasible, to the robot by warping the motion’s time line so that the motion trajectory will remain the same but the velocity and acceleration profiles will be changed. The second method generates bipedal locomotion for given footsteps. All the proposed motion controllers and generators are applicable to general scenarios including uneven terrains and motions with the support of other links besides feet.

New computational method for three-fingered force-closure test

This paper proposes an efficient implementation of a force-closure test for frictional three-finger grasps. The implementation is based on a condition that transforms force-closure testing into the problem of convex hull intersection in projective space. The proposed implementation further reduces the problem into the problem of computing whether a line segment intersects a convex hull of at most four points. Implementation results are presented along with a thorough performance analysis and comparison with several existing methods. The results are also verified with arbitrary precision floating point computation. This provides comparison of qualitative error resulting from floating point roundoff. The result shows that the proposed implementation outperforms other methods in terms of speed and precision.