Patrick M. Wensing

Generation of dynamic humanoid behaviors through task-space control with conic optimization

This paper presents a new formulation of prioritized task-space control for humanoids that is used to develop a dynamic kick and dynamic jump in a 26 degree of freedom simulated system. The demonstrated motions are controlled through a real-time conic optimization scheme that selects appropriate joint torques and contact forces. More specifically, motions are characterized in appropriate task spaces, and the real-time optimizer solves the task-space control problem while accounting for user-defined priorities between the tasks. In contrast to previous solutions of the Prioritized Task-Space Control (PTSC) problem for humanoids, the solution presented here satisfies the ZMP constraint and ground friction limitations at all levels of priority, and is general to periods of flight as well as support. All generated motions include control of the systems centroidal angular momentum, which leads to emergent whole-body behaviors, such as arm-swing, that are not specified by the designer. In addition, compared to a previous quadratic programming solution of the PTSC problem, our approach gains a factor of 2 speedup in its required computational time. This speedup allows the control approach to operate at real-time rates of approximately 200 Hz.

Online Planning for Autonomous Running Jumps Over Obstacles in High-Speed Quadrupeds

United States. Defense Advanced Research Projects Agency. Maximum Mobility and Manipulation (M3) Program

3D-SLIP steering for high-speed humanoid turns

This paper presents new methods to control humanoid turns while running, through the use of a 3D-SLIP template model with steering control. The work builds on a previous controller for straight-ahead running and describes the new methods that enable online humanoid steering for different speeds and turn rates. As opposed to previous research which has studied 3D-SLIP steering with a monopod model, motion optimization for the SLIP here enforces leg separation. This leg separation gives rise to body sway in forward running and allows the template to capture the unique roles that the inside and outside legs each play during a high-speed turn. The trajectory optimization approach for this template is given, and the resultant CoM trajectories are characterized. Modifications to a previous controller for straight-ahead running are shown to enable running turns in a simulated humanoid model. The methods allow the humanoid to change its turn rate and direction from step to step and enable execution of a high-speed turn with a radius that is one fourth that of a standard 400m track. A video attachment to this paper shows the humanoid turning while running at up to 4.0 m/s, and highlights its ability to maintain balance in spite of push disturbances.

Terrain-Blind Humanoid Walking Based on a 3-D Actuated Dual-SLIP Model

While a number of controllers exist for dynamic humanoid walking over known uneven terrain, the ability to negotiate moderate changes in ground height without environment perception is still lacking. Such capability would mitigate problems caused by inaccurate sensing and reduce online terrain-dependent computational requirements. This letter proposes a 1-step terrain adaptation strategy for humanoid walking based on the 3-D actuated Dual-SLIP model. A flexible gait to negotiate unknown terrain is synthesized from a series of consistent gait adaptations acquired from off-line optimization with this simple model. Being open-loop prior to touchdown, the strategy requires no perception of the terrain. Also, the resultant terrain-robust swing foot trajectory exhibits human-like characteristics such as leg retraction and extension near the end of the swing phase. Through a task-space control framework, the model-derived gait is embedded into the high-DoF ATLAS humanoid model. In the final result, a “blindfolded” ATLAS model reliably walks over randomly generated uneven terrain (with per-step height changes of up to 5% of the leg length) at a constant midstance speed.

Trajectory generation for dynamic walking in a humanoid over uneven terrain using a 3D-actuated Dual-SLIP model

The Dual-SLIP model has been proposed as a walking template that inherently encodes a rich set of human-like features. Previous work has used the 3D Dual-SLIP with bio-inspired leg actuation to generate a human-like dynamic walking gait over a wide range of speeds. The work presented in this paper extends the 3D Dual-SLIP walking strategy to uneven terrain. With nonlinear optimization based on a multiple-shooting formulation, actuated Dual-SLIP walking gaits over uneven terrain are identified that handle 1-step elevation changes up to ±10 cm. Moreover, this Dual-SLIP actuation strategy enables a constant center of mass (CoM) forward speed at leg midstance to be maintained. The resultant gaits have revealed a leg lengthening/shortening strategy that is similar to that adopted by a human when walking over prepared, uneven terrain. Results demonstrate that the CoM trajectories and ground reaction force patterns found with the approach are comparable to the human data found in the biomechanics literature. The trajectories generated by the Dual-SLIP model are also demonstrated to orchestrate a dynamic walking motion with an anthropomorphic humanoid model in simulation over uneven terrain.

OPTIMIZING FOOT CENTERS OF PRESSURE THROUGH FORCE DISTRIBUTION IN A HUMANOID ROBOT

The force distribution problem (FDP) in robotics requires the determination of multiple contact forces to match a desired net contact wrench. For the double support case encountered in humanoids, this problem is underspecified, and provides the opportunity to optimize desired foot centers of pressure (CoPs) and forces. In different contexts, we may seek CoPs and contact forces that optimize actuator effort or decrease the tendency for foot roll. In this work, we present two formulations of the FDP for humanoids in double support, and propose objective functions within a general framework to address the variety of competing requirements for the realization of balance. As a key feature, the framework is capable to optimize contact forces for motions on uneven terrain. Solutions for the formulations developed are obtained with a commercial nonlinear optimization package and through analytical approaches on a simplified problem. Results are shown for a highly dynamic whole-body humanoid reaching motion performed on even terrain and on a ramp. A convex formulation of the FDP provides real-time solutions with computation times of a few milliseconds. While the convex formulation does not include CoPs explicitly as optimization variables, a novel objective function is developed which penalizes foot CoP solutions that approach the foot boundaries.

Improved Computation of the Humanoid Centroidal Dynamics and Application for Whole-Body Control

The control of centroidal momentum has recently emerged as an important component of whole-body humanoid control, resulting in emergent upper-body motions and increased robustness to pushes when included in whole-body frameworks. Previous work has developed specialized computational algorithms for the centroidal momentum matrix (CMM) and its derivative, which relate rates of change in centroidal momentum to joint rates and accelerations of the humanoid. This paper instead shows that specialized algorithms are in fact not always required. Since the dynamics of the centroidal momentum are embedded in the joint-space dynamic equations of motion, the CMM and terms involving its derivative can be computed from the joint-space mass matrix and Coriolis terms. This new approach presents improvements in terms of its generality, compactness, and efficiency in comparison to previous specialized algorithms. The new computation method is then applied to perform whole-body control of a dynamic kicking motion, where the mass matrix and Coriolis terms are already required by the controller. This example motivates how centroidal momentum can be used as an aggregate descriptor of motion in order to ease whole-body motion authoring from a task-space perspective. It further demonstrates emergent upper-body motion from centroidal angular momentum (CAM) control that is shown to provide desirable regulation of the net yaw moment under the foot. Finally, a few perspectives are provided on the use of centroidal momentum control.

Dynamic walking in a humanoid robot based on a 3D Actuated Dual-SLIP model

This paper presents a method for the generation of dynamic walking gaits with a 3D Dual-SLIP model and its application to a simulated Hubo+ based humanoid. Previous approaches with the Dual-SLIP model have only focused on the planar case, wherein self-stable gaits can be found. When extended to 3D here, this model has not been found to exhibit self-stable gaits, requiring new methods for gait optimization and control. By taking advantage of a newly discovered symmetry condition for the Dual-SLIP model, this work proposes a quarter period (half step) optimization process to find periodic walking gaits in 3D. An LQR controller is developed to regulate the state of the model at leg midstance (MS) based on its return map dynamics. The Dual-SLIP model is extended by introducing a bio-inspired leg length actuation scheme in order to describe high-speed walking gaits (up to 2 m/s for human-compatible parameters). Finally, the CoM trajectory and footstep positions from the 3D Dual-SLIP are used as a reference in a task-space controller with a Hubo+ based humanoid model. By tracking these references, the methods successfully produce human-like dynamic walking gaits in simulation which are robust to disturbances. The whole-body control system for walking can handle uneven terrain with variation up to 10% of its leg length. This represents the first humanoid dynamic walking approach based on a 3D Dual-SLIP model.

High-speed bounding with the MIT Cheetah 2: Control design and experiments

This paper presents the design and implementation of a bounding controller for the MIT Cheetah 2 and its experimental results. The paper introduces the architecture of the controller along with the functional roles of its subcomponents. The application of impulse scaling provides feedforward force profiles that automatically adapt across a wide range of speeds. A discrete gait pattern stabilizer maintains the footfall sequence and timing. Continuous feedback is layered to manage balance during the stance phase. Stable hybrid limit cycles are exhibited in simulation using simplified models, and are further validated in untethered three-dimensional bounding experiments. Experiments are conducted both indoors and outdoors on various man-made and natural terrains. The control framework is shown to provide stable bounding in the hardware, at speeds of up to 6.4 m/s and with a minimum total cost of transport of 0.47. These results are unprecedented accomplishments in terms of efficiency and speed in untethered experimental quadruped machines.

Development of high-span running long jumps for humanoids

This paper presents new methods to develop a running long jump for a simulated humanoid robot. Starting from a steady-state running motion, a new spring loaded inverted pendulum (SLIP) based 3D template model for a running jump is presented. The use of this model is motivated by a simpler model from biomechanics which describes the dynamics of human long jumpers in the sagittal plane. While previously only used to describe the thrust step of a long jump, this type of model is also shown to generate useful Center of Mass (CoM) trajectories to return to steady-state running upon landing. A principled optimization approach for this new template is described to generate reference CoM trajectories for maximum span which are able to be kinematically and dynamically retargeted to the humanoid. The key features of an optimal long jump are highlighted, and a task-space control approach to realize the motion on a humanoid is summarized. A video attachment to this paper shows an optimal long jump for a 6 m/s approach speed, where the humanoid is able to clear a large gap, and highlights the effects of non-optimal takeoff-velocity angles.