Katja D. Mombaur

From human to humanoid locomotion--an inverse optimal control approach

The purpose of this paper is to present inverse optimal control as a promising approach to transfer biological motions to robots. Inverse optimal control helps (a) to understand and identify the underlying optimality criteria of biological motions based on measurements, and (b) to establish optimal control models that can be used to control robot motion. The aim of inverse optimal control problems is to determine—for a given dynamic process and an observed solution—the optimization criterion that has produced the solution. Inverse optimal control problems are difficult from a mathematical point of view, since they require to solve a parameter identification problem inside an optimal control problem. We propose a pragmatic new bilevel approach to solve inverse optimal control problems which rests on two pillars: an efficient direct multiple shooting technique to handle optimal control problems, and a state-of-the art derivative free trust region optimization technique to guarantee a match between optimal control problem solution and measurements. In this paper, we apply inverse optimal control to establish a model of human overall locomotion path generation to given target positions and orientations, based on newly collected motion capture data. It is shown how the optimal control model can be implemented on the humanoid robot HRP-2 and thus enable it to autonomously generate natural locomotion paths.

Online Walking Motion Generation with Automatic Foot Step Placement

The goal of this paper is to demonstrate the capacity of model predictive control (MPC) to generate stable walking motions without the use of predefined footsteps. Building up on well-known MPC schemes for walking motion generation, we show that a minimal modification of these schemes allows designing an online walking motion generator that can track a given reference speed of the robot and decide automatically the footstep placement. Simulation results are proposed on the HRP-2 humanoid robot, showing a significant improvement over previous approaches.

Online walking gait generation with adaptive foot positioning through Linear Model Predictive control

Building on previous propositions to generate walking gaits online through the use of linear model predictive control, the goal of this paper is to show that it is possible to allow on top of that a continuous adaptation of the positions of the foot steps, allowing the generation of stable walking gaits even in the presence of strong perturbations, and that this additional adaptation requires only a minimal modification of the previous schemes, especially maintaining the same linear model predictive form. Simulation results are proposed then on the HRP-2 humanoid robot, showing a significant improvement over the previous schemes.

Modeling and Optimal Control of Human-Like Running

Designing and controlling an anthropomorphic mechatronic system that is able to perform a dynamic running motion is a challenging task. One difficulty is that the fundamental principles of natural human running motions are not yet fully understood. The purpose of this paper is to show that mathematical optimization is a helpful tool to gain this insight into fast and complex motions. We present physics-based running motions for complex models of human-like running in three dimensions that have been generated by optimization. Running is modeled as a multiphase periodic motion with discontinuities, based on multibody system models of the locomotor system with actuators and spring-damper elements at each joint. The problem of generating gaits is formulated as offline optimal control problem and solved by an efficient direct multiple shooting method. We present optimization results using energy-related criteria and show that they have a close resemblance to running motions of humans. The results provide information about the internal forces and torques required to produce natural human running, as well as on the resulting kinematics.

Open-loop stable running

We present simulated monopedal and bipedal robots that are capable of open-loop stable periodic running motions without any feedback even though they have no statically stable standing positions. Running as opposed to walking involves flight phases which makes stability a particularly difficult issue. The concept of open-loop stability implies that the actuators receive purely periodic torque or force inputs that are never altered by any feedback in order to prevent the robot from falling. The design of these robots and the choice of model parameter values leading to stable motions is a difficult task that has been accomplished using newly developed stability optimization methods.

Using optimization to create self-stable human-like running

This paper demonstrates how numerical optimization techniques can efficiently be used to create self-stable running motions for a human-like robot model. Exploitation of self-stability is considered to be a crucial factor for biological running and might be the key for success to make bipedal and humanoid robots run in the future. We investigate a two-dimensional simulation model of running with nine bodies (trunk, thighs, shanks, feet, and arms) powered by external moments at all internal joints. Using efficient optimal control techniques and stability optimization, we were able to determine model parameters and actuator inputs that lead to fully open-loop stable running motions.

Prediction of Stable Walking for a Toy That Cannot Stand

Previous experiments [M. J. Coleman and A. Ruina, Phys. Rev. Lett. 80, 3658 (1998)] showed that a gravity-powered toy with no control and that has no statically stable near-standing configurations can walk stably. We show here that a simple rigid-body statically unstable mathematical model based loosely on the physical toy can predict stable limit-cycle walking motions. These calculations add to the repertoire of rigid-body mechanism behaviors as well as further implicating passive dynamics as a possible contributor to stability of animal motions.

Self-stabilizing somersaults

We investigate the open-loop stability of a planar biped robot performing a periodic motion of forward somersaults with alternating single-leg contacts. The robot has a trunk and two actuated telescopic legs with point feet which are coupled to the trunk by actuated hinges. There is compliance and damping in the hip and in the legs. The concept of open-loop control implies that all actuators of the system receive predetermined inputs that are never altered by any feedback interference. Only with the right choice of model parameters and actuator inputs is it possible to create such self-stabilizing motions exploiting the natural stability properties of the system. These unknowns have been determined using special-purpose stability-optimization methods. The resulting motion is not only stable, but also a more efficient form of forward motion than running for the investigated robot.

A Reactive Walking Pattern Generator Based on Nonlinear Model Predictive Control

The contribution of this work is to show that real-time nonlinear model predictive control (NMPC) can be implemented on position controlled humanoid robots. Following the idea of “walking without thinking,” we propose a walking pattern generator that takes into account simultaneously the position and orientation of the feet. A requirement for an application in real-world scenarios is the avoidance of obstacles. Therefore, this letter shows an extension of the pattern generator that directly considers the avoidance of convex obstacles. The algorithm uses the whole-body dynamics to correct the center of mass trajectory of the underlying simplified model. The pattern generator runs in real-time on the embedded hardware of the humanoid robot HRP2 and experiments demonstrate the increase in performance with the correction.

Human-like actuated walking that is asymptotically stable without feedback

Studies a two-legged kneed walking robot with point feet. At any given moment, only one foot is in contact with the ground, and the switching is instantaneous. The robot can be considered as a simplified model of human walking. The periodic torque histories applied to each link are a priori prescribed for a motion and are not changed by any feedback interference. Nevertheless the robot is capable of naturally recovering from perturbations, returning to standard gait-a property that we call open-loop stable. We formulate the problem of open-loop stabilization as an optimal control problem. Design parameters and periodic torque inputs that lead to a stable configuration are computed using a two-level optimization procedure. We believe that this is the first demonstration of the ability to create stable actuated open-loop gaits of bipedal walking robots.