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Collaboration between humans and robots is an important aspect of Industry 4.0. It can be improved by incorporating human-like characteristics into robot motion planning. It is assumed that humans move optimal with respect to a certain objective or cost function. To find this function, also for a robot, we use an inverse optimal control approach identifying what linear weighted combination of physically interpretable cost functions best mimics human point-to-point motions. A bi-level optimization is used, where the upper level compares the optimal robot result of the lower level with human reference motions. Two depth cameras are combined in a setup to record these reference motions. The resulting weighted cost functions are then used to generate new motions for a seven degrees of freedom robot arm. The resulting optimized motions are compared to standard robot motions based on linear interpolation in joint or task space. The comparison is performed by means of a small experiment where preliminary observations show that humans experience these motions as more anthropomorphic and feel at least equally comfortable and safe compared to existing motion planning strategies.

Operating times of several years indicate a high influence of energy consumption on the resource efficiency of a robotic system. Consequently, the energy efficiency is addressed by various methods related to the improvement of hardware or to optimal motion planning. However, the service life and a potential prolongation impact the resource efficiency as well. Correspondingly, a multi-objective trajectory optimization allows to consider energy consumption and expected service life in conjunction. To this end, both criteria are modeled based on the structure and components of an exemplary manipulator. Simplifications of the objective function are proposed for optimization purposes. Corresponding results for an exemplary task are discussed and indicate the feasibility of the simplified objective function. Furthermore, the results highlight a large potential of increased service life as well as a conflict of interest, as maximizing the service life comes at the cost of increased energy consumption. Thus, the combined optimization of energy consumption and service life indicates the importance of considering both criteria in order to contribute to the overall resource efficiency of the system.

Modern industry benefits from the automation capabilities and flexibility of robots. Consequently, the performance depends on the individual task, robot and trajectory, while application periods of several years lead to a significant impact of the use phase on the resource efficiency. In this work, simulation models predicting a robot’s energy consumption are extended by an estimation of the reliability, enabling the consideration of maintenance to enhance the assessment of the application’s life cycle costs. Furthermore, a life cycle assessment yields the greenhouse gas emissions for the individual application. Potential benefits of the combination of motion simulation and cost analysis are highlighted by the application to an exemplary system. For the selected application, the consumed energy has a distinct impact on greenhouse gas emissions, while acquisition costs govern life cycle costs. Low cycle times result in reduced costs per workpiece, however, for short cycle times and higher payloads, the probability of required spare parts distinctly increases for two critical robotic joints. Hence, the analysis of energy consumption and reliability, in combination with maintenance, life cycle costing and life cycle assessment, can provide additional information to improve the resource efficiency.

Robot application developers program industrial robots during the commissioning or re-configuration of a production line. Not only do they require precise locations of work pieces and respective movements but also need to optimize program parameters manually. This often results in high engineering effort and stress. This paper introduces an approach to support robot application developers using distributed learning and machine learning to optimize robot application parameters in simulation. Contrary to end-to-end robot learning approaches which are often infeasible to adopt in practice, this approach leverages domain knowledge of application developers and their familiarity with writing robot programs. The developer is only additionally required to specify bounds for parameters to be optimized and an evaluation criterion. A central machine triggers as many worker machines as required to run simulations in parallel with different parameters to learn the best policy. Our approach works independent of the robot task and robot simulation software and can be configured with different algorithms. To validate the approach, it is applied to a robotic insertion task in an assembly scenario using a genetic algorithm and ABB RobotStudio.

Lower limb exoskeletons provide a promising approach to allow disabled people to walk again in the future. Designing such exoskeletons and tuning the required actuators is challenging, since the fu...

We combine optimal control and movement primitive learning in a novel way for the fast generation of humanoid walking movements and demonstrate our approach at the example of the humanoid robot HRP-2 with 36 degrees of freedom. The present framework allows for an efficient computation of long walking sequences consisting of feasible steps of different kind: starting steps from a static posture, cyclic steps or steps with varying step lengths, and stopping motions back to a static posture. Together with appropriate sensors and high level decision strategies this approach provides an excellent basis for an adaptive walking generation on challenging terrain. Our framework comprises a movement primitive model learned from a small number of example steps that are dynamically feasible and minimize an integral mean of squared torques. These training steps are computed by solving three different kinds of optimal control problems that are restricted by the whole-body dynamics of the robot and the gait cycle. The movement primitive model decomposes the joint angles, pelvis orientation and ZMP trajectories in the example data into a small number of primitives, which effectively deals with the redundancy inherent in highly articulated motion. New steps can be composed by weighted combinations of these primitives. The mappings from step parameters to weights are learned with a Gaussian process approach, the contiguity of subsequent steps is promoted by conditioning the beginning of a new step on the end of the current one. Each step can be generated in less than a second, because the expensive optimal control computations, which take several hours per step, are shifted to the precomputational off-line phase. We validate our approach in the virtual robot simulation environment OpenHRP and study the effects of different kernels and different numbers of primitives. We show that the robot can execute long walking sequences with varying step lengths without falling, and hence that feasibility is transferred from optimized to generated motions. Furthermore, we demonstrate that the generated motions are close to torque optimality on the interior parts of the steps but have higher torques than their optimized counterparts on the steps boundaries. Having passed the validation in the robot simulator, we plan to tackle the transfer of this approach to the real platform HRP-2 as a next step.

We study how humans performing periodic walking motions react to strong perturbations that are applied in form of pushes from behind. We propose a computational method that allows to generate optimal recovery motions based on a dynamic multi-body model of the human walking process. The assumption is that humans in such a situation would aim to pursue the walking motions while at the same time limiting the effort for the motion. For a given position and velocity in the middle of a periodic walking motion and a given pushing force profile, magnitude and contact point we determine the motion of the human model that minimizes a combined criterion joint torques and a deviation from periodicity. The recovery horizon considered in the multiphase optimal control problem is one step. The optimal control problem is solved using a direct boundary value problem approach based on multiple shooting. We present resulting optimal recovery motions for pushing forces between 150 N and 600 N which all look realistic. The proposed method has potential applications in the computation of push recovery motions for humanoid robots or for elderly humans with physical assistive devices, in each case applied to the respective model.

A novel indirect force control scheme for rigid manipulators is presented. The approach is based on wellknown proportional Cartesian force controllers. However, the new concept integrates Cartesian force control and mapping from Cartesianto joint-space into a dynamic state-space controller. This allows interpreting the tasks of force controller parameterization and mapping to joint space as an eigenstructure assignment problem. Guidelines for practical force controller tuning are given. The proposed control approach has been verified in several experimental results gathered on an ABB YuMi, a redundant dual-arm manipulator.

Strain wave gears are frequently used in small and medium size industrial robots. In order to describe and quantify friction effects in gearboxes of such type, a structurally simple, yet powerful model is proposed taking into account both speed-and load-dependent friction effects. Moreover, position-dependent disturbances in a robotic joint are considered. An identification procedure is presented that allows to separate the individual components of the model and identify them subsequently. The effectiveness of the model and identification procedure is validated using experimental data gathered from four different robotic joints of varying size. Furthermore, the benefits of improved friction modeling are shown by means of different applications, including smooth lead-through programming and sensorless force control.

International audience; COCoMoPL [6] is a recently developed approach Combining Optimal Control, Movement Primitives and Learning for the generation of humanoid walking motions. It solves optimal control problems based on detailed dynamic models of the robot for a variety of walking parameters and uses the solutions as training data to create movement primitives that are very close to feasibility and optimality. These can be employed to synthesize complex walking sequences for humanoid robots online in a very efficient way. We demonstrate, for the first time, that COCoMoPL works on a real humanoid robot, here HRP-2 with 36 DOF and 30 position controlled actuators. To this end, it was necessary to significantly extend the existing approach by including transition steps into the training data, modify the movement primitives (MP) to admit these transitions, improve the representation of the ZMP MPs and tighten the transition conditions at the beginning and end of steps. We present a thorough validation of the method in simulation and on the real robot for a challenging sequence of movements. We also compare the characteristics of movements after each step of the methodology.

We formulate and solve an inverse optimal control problem that allows us to study human gait based on motion capture data and a template model that is defined by a simple mechanical model of walking with two elastic legs. To this end we derive an optimal control model that consists of two parts: a three-dimensional template walker and an objective, defined by a linear combination of physically meaningful optimization criteria known from humanoid robotics. Based on a direct all-at-once approach we identify the objective weights such that the resulting optimal gait fits real human motion data as closely as possible. Considering knee actuation, foot placement and phase duration as controls we identify the optimal weights for six different trials on level ground from two very different subjects. In future work the identified criteria will be used to simulate optimized human gait and to generate reference trajectories for humanoid gait control.

In this paper, we discuss numerical foundations and computational results for inverse optimal control of human locomotion based on human motion capture data. The task of inverse optimal control is to identify the precise underlying objective function that is optimized in an observed motion. The presented methods can cope with partial and imprecise measurements of the state variables which is typically the case for motion capture recordings. We investigate human walking and running motions on different levels of detail and consequently different underlying models which all have their own motivation depending on the question asked. Whole-body models are used to explore the mechanisms of motions on joint level, while simple models describing the subject as a single entity can be used to describe overall locomotion behavior. At an intermediate level, template models describe some relative motions of bodies while maintaining simplicity and computational efficiency. Results will be presented for all model types and different walking tasks. We also show for some of them how the identified objective functions can be used to generate new waking motions for humanoid robots in novel scenarios.

Benchmarking bipedal locomotion is an important topic not only for wearable robotics, but also for human movement analysis and humanoid robotics. In this paper we discuss how data from the KoroiBot walking database can be used to establish benchmarking data for human walking in different situations based on direct extraction and on model-based analysis. The goal is to identify human reference values for important quantities defining walking motions which can then serve for evaluating walking motions in the different areas of applications.

In this paper we present an inverse optimal control based transfer of motions from human experiments to humanoid robots and apply it to walking in constrained environments. To this end we introduce a 3D template model, which describes motion on the basis of center of mass trajectory, foot trajectories, upper body orientation and phase duration. Despite of its abstract architecture with prismatic joints combined with damped series elastic actuators instead of knees, the model (including dynamics and constraints) is suitable to describe both, human and humanoid locomotion with appropriate parameters. We present and apply an inverse optimal control approach to identify optimality criteria based on human motion capture experiments. The identified optimal strategy is then transferred to the humanoid robot for gait generation by solving an optimal control problem, which takes into account the properties of the robot and differences in the environment. The results of this approach are the center of mass trajectory, the foot trajectories, the torso orientation, and the single and double support phase durations for a sequence of multiple steps allowing the humanoid robot to walk within a new environment. We present one computational cycle (from motion capture data to an optimized robot motion) for the example of walking over irregular step stones with the aim to transfer the motion to two very different humanoid robots (iCub Heidelberg01 and HRP-2 14). The transfer of these optimized robot motions to the real robots by means of inverse kinematics is work in progress and not part of this paper.

Understanding the underlying concepts of human locomotion is important for many fields of research. Based on the assumption that human motions are optimal, we propose an inverse optimal control (IOC) based approach to identify the optimality criteria in human walking. To this end, human walking is modeled as a non-linear optimal control problem with a linear combination of elementary optimality functions as objective and a hybrid dynamics multi-body system as constraints. The developed IOC-framework is set up in a modular way and exploits the natural bi-level structure of the problem. It allows for a great flexibility in the choice of outer optimization techniques and inner dynamic models. In the present work, we use the developed IOC approach to identify weights of seven elementary criteria for seven walking motions captured from six different subjects. The considered optimality criteria address the minimization of joint torques for four sets of joints, head stabilization, the step length, and the step frequency. For all trials the algorithm performs successfully. Even though the identified weights differ observably between subjects, which explains the different walking styles, the correlation matrix gives rise to the hypothesis that there exists a significant correlation of optimality across subjects. The identification of optimality criteria in human walking is a very important issue for all disciplines, where a prediction of human behavior is needed. For example in medical applications to improve therapies or to develop new mobility devices, in sport science to improve training plans or in humanoid robotics to develop new walking strategies.

SUMMARY This paper is motivated by an optimal boundary control problem for the cooling process of molten and already formed glass down to room temperature. The high temperatures at which glass is processed demand to include radiative heat transfer in the computational model. Since the complete radiative heat transfer equations are too complex for optimization purposes, we use simplified approximations of spherical harmonics coupled with a practically relevant frequency bands model. The optimal control problem is considered as a partial differential algebraic equation (PDAE)-constrained optimization problem with box constraints on the control. In this paper, we augment the objective by a functional depending on the state gradient, which forces a minimization of thermal stress inside the glass. To guarantee consistent and grid-independent values of the reduced objective gradient at the end of the cooling process, we pursue two approaches. The first includes the temperature gradient with a time-dependent linearly decreasing weight. In the second approach, we augment the objective functional by the final state tracking and final state gradient optimization. To determine an optimal boundary control, we apply a projected gradient method with the Armijo step size rule. The reduced objective gradient is computed by the continuous adjoint approach. The arising time-dependent PDAEs are numerically solved by variable step size one-step methods of Rosenbrock type in time and adaptive multilevel finite elements in space. We present two-dimensional numerical results for an infinitely long glass block and compare the two different approaches derived to ensure consistency at the end of the cooling process. Copyright © 2011 John Wiley & Sons, Ltd.

We present an adaptive multilevel generalized SQP method to solve PDAE-constrained optimization problems. It explicitly allows the use of independent integration schemes such that all involved systems can be solved highly efficient and as accurate as desired. We will couple the optimization with the state-of-the-art PDAE solver KARDOS and apply the new tool to a radiative heat transfer problem described by space-time dependent non-linear partial differential algebraic equations. Results are presented, compared and discussed.

We present a new approach for humanoid gait generation based on movement primitives learned from optimal and dynamically feasible motion trajectories. As testing platform we consider the humanoid robot HRP-2, so far only in simulation. Training data is generated by solving a set of optimal control problems for a minimum-torque optimality criterion and five different step lengths. As the dynamic robot model with all its kinematic and dynamic constraints is considered in the optimal control problem formulation, the resulting motion trajectories are not only optimal but also dynamically feasible. For the learning process we consider the joint angle trajectories of all actuated joints, the ZMP trajectory and the pelvis trajectory, which are sufficient quantities to control the robot. From the training data we learn morphable movement primitives based on Gaussian processes and principal component analysis. We show that five morphable primitives are sufficient to generate steps with 24 different lengths, which are close enough to both dynamical feasibility and optimality to be useful for fast on-line movement generation.

We present an adaptive multilevel optimization approach which is suitable to solve complex real-world optimal control problems for time-dependent nonlinear partial differential algebraic equations with point-wise constraints on control and state. Relying on Moreau-Yosida regularization, the multilevel SQP method presented in Clever et al. (Generalized multilevel SQP-methods for PDAE-constrained optimization based on space-time adaptive PDAE solvers. In: Constrained optimization and optimal control for partial differential equations. Volume 160 of International series of numerical mathematics. Springer, Basel, pp 37–60, 2012) is extended to the state-constrained case. First-order convergence results are shown. The new multilevel SQP method is combined with the state-of-the-art software package KARDOS to allow the efficient resolution of different space and time scales in an adaptive manner. The numerical performance of the method is demonstrated and analyzed for a real-life three-dimensional radiative heat transfer problem modeling the cooling process in glass manufacturing and a two-dimensional thermistor problem modeling the heating process in steel hardening.

Human movement, as for example human gait, can be considered as an optimal realization of some given task. However, the criterion for which the naturally performed human motion is optimal, is generally not known. In this article we formulate an inverse optimal control problem to study the relevance of four different optimization criteria in human locomotion. As a walking model we use an actuated three dimensional spring loaded inverted pendulum (3D-SLIP), which is able to mirror the typical shape of the center of mass trajectory in human gait. Using a direct all-at-once approach, the weighting of the optimization criteria and the position of the footsteps are optimized in such a way, that the center of mass trajectory of the resulting optimal state fits real motion capture data as good as possible. Numerical experiments show, that whereas the so called capture point seems to have a great impact on human walking, minimization of the vertical center of mass movement does not show any relevance at all. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this work, we present an all-in-one optimization approach suitable to solve complex optimal control problems with time-dependent nonlinear partial differential algebraic equations and point-wise control constraints. A newly developed generalized SQP-method is combined with an error based multilevel strategy and the state-of-the-art software package Kardos to allow the efficient resolution of different space and time scales in an adaptive manner. The numerical performance of the method is demonstrated and analyzed for a real-life two-dimensional radiative heat transfer problem modelling the optimal boundary control for a cooling process in glass manufacturing.

We have developed a fully adaptive optimization environment suitable to solve complex optimal control problems restricted by partial differential algebraic equations (PDAEs) and pointwise constraints on the control [1, 2]. This contribution is devoted to the inclusion of pointwise constraints on the state within the optimization environment. To this end we first give a brief introduction into the architecture of the environment and the inclusion of pointwise constraints on the state by Moreau-Yosida regularization. Then, we test the new tool by applying it to an optimal boundary control problem for the cooling of hot glass down to room temperature, modeled by radiative heat transfer and semi-transparent boundary conditions. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

We present a model hierarchy multilevel optimisation approach to solve an optimal boundary control problem in glass manufacturing. The process is modelled by radiative heat transfer and formulated as an optimal control problem restricted by partial differential algebraic equations (PDAEs) and additional control constraints. We consider a sequence of model approximations given by space-time dependent non-linear PDAEs of ascending accuracy. The different models allow for a model hierarchy-based optimisation approach, where the models are shifted automatically as the optimisation proceeds. We present a realisation of a multilevel generalised SQP method within the fully space-time adaptive optimisation environment Kardos using linearly implicit methods of Rosenbrock type and multilevel finite elements. We apply the optimal control algorithm to a glass cooling problem and present numerical experiments for the model hierarchy-based approach in two spatial dimensions and for a fully space-time adaptive optimisation in three spatial dimensions.

We give an overview about several verification tools to study consistency between discrete optimization problem and discrete derivatives when using independent discretization schemes for state and adjoint systems within the context of optimal control problems. We present strategies that detect impreciseness within a considered quantity without any additional effort. They are therefore a suitable tool to control the grid refinement within a multilevel setting. More detailed tools are useful to verify the problem implementation and to analyze the quantities discretization error order. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

In order to be useful in daily life, lower limb exoskeletons have to be able to provide support not only for nominal situations, such as level ground walking, but also for the recovery from extreme situations. In this paper, we investigate which torques a lower leg exoskeleton would have to produce in order to allow a person to recover from large perturbations or pushes that may occur while walking. We propose a model-based optimization approach that takes into account dynamic models of the human and the exoskeleton as well as experimental data of humans being pushed. Using optimal control and a least squares objective function we compute the joint torques that exoskeletons of different masses and mass distributions would have to produce in order to make the person follow the recorded recovery trajectories of healthy subjects and which loads would occur in the structure. The results of these computations can serve as guidelines for the design of future lower limb exoskeletons.