On Time Optimization of Centroidal Momentum Dynamics

Recently, the centroidal momentum dynamics has received substantial attention to plan dynamically consistent motions for robots with arms and legs in multi-contact scenarios. However, it is also non convex which renders any optimization approach difficult and timing is usually kept fixed in most trajectory optimization techniques to not introduce additional non convexities to the problem. But this can limit the versatility of the algorithms. In our previous work, we proposed a convex relaxation of the problem that allowed to efficiently compute momentum trajectories and contact forces. However, our approach could not minimize a desired angular momentum objective which seriously limited its applicability. Noticing that the non-convexity introduced by the time variables is of similar nature as the centroidal dynamics one, we propose two convex relaxations to the problem based on trust regions and soft constraints. The resulting approaches can compute time-optimized dynamically consistent trajectories sufficiently fast to make the approach realtime capable. The performance of the algorithm is demonstrated in several multi-contact scenarios for a humanoid robot. In particular, we show that the proposed convex relaxation of the original problem finds solutions that are consistent with the original non-convex problem and illustrate how timing optimization allows to find motion plans that would be difficult to plan with fixed timing.Comment: 7 pages, 4 figures, ICRA 201

Humanoid Momentum Estimation Using Sensed Contact Wrenches

This work presents approaches for the estimation of quantities important for the control of the momentum of a humanoid robot. In contrast to previous approaches which use simplified models such as the Linear Inverted Pendulum Model, we present estimators based on the momentum dynamics of the robot. By using this simple yet dynamically-consistent model, we avoid the issues of using simplified models for estimation. We develop an estimator for the center of mass and full momentum which can be reformulated to estimate center of mass offsets as well as external wrenches applied to the robot. The observability of these estimators is investigated and their performance is evaluated in comparison to previous approaches.Comment: Submitted to the 15th IEEE RAS Humanoids Conference, to be held in Seoul, Korea on November 3 - 5, 201

Automatic Gain Tuning of a Momentum Based Balancing Controller for Humanoid Robots

This paper proposes a technique for automatic gain tuning of a momentum based balancing controller for humanoid robots. The controller ensures the stabilization of the centroidal dynamics and the associated zero dynamics. Then, the closed-loop, constrained joint space dynamics is linearized and the controller's gains are chosen so as to obtain desired properties of the linearized system. Symmetry and positive definiteness constraints of gain matrices are enforced by proposing a tracker for symmetric positive definite matrices. Simulation results are carried out on the humanoid robot iCub.Comment: Accepted at IEEE-RAS International Conference on Humanoid Robots (HUMANOIDS). 201

Optimal Reduced-order Modeling of Bipedal Locomotion

State-of-the-art approaches to legged locomotion are widely dependent on the use of models like the linear inverted pendulum (LIP) and the spring-loaded inverted pendulum (SLIP), popular because their simplicity enables a wide array of tools for planning, control, and analysis. However, they inevitably limit the ability to execute complex tasks or agile maneuvers. In this work, we aim to automatically synthesize models that remain low-dimensional but retain the capabilities of the high-dimensional system. For example, if one were to restore a small degree of complexity to LIP, SLIP, or a similar model, our approach discovers the form of that additional complexity which optimizes performance. In this paper, we define a class of reduced-order models and provide an algorithm for optimization within this class. To demonstrate our method, we optimize models for walking at a range of speeds and ground inclines, for both a five-link model and the Cassie bipedal robot.Comment: Submitted to ICRA 202

Sequential Motion Planning for Bipedal Somersault via Flywheel SLIP and Momentum Transmission with Task Space Control

In this paper, we present a sequential motion planning and control method for generating somersaults on bipedal robots. The somersault (backflip or frontflip) is considered as a coupling between an axile hopping motion and a rotational motion about the center of mass of the robot; these are encoded by a hopping Spring-loaded Inverted Pendulum (SLIP) model and the rotation of a Flywheel, respectively. We thus present the Flywheel SLIP model for generating the desired motion on the ground phase. In the flight phase, we present a momentum transmission method to adjust the orientation of the lower body based on the conservation of the centroidal momentum. The generated motion plans are realized on the full-dimensional robot via momentum-included task space control. Finally, the proposed method is implemented on a modified version of the bipedal robot Cassie in simulation wherein multiple somersault motions are generated