Research papers and code for "Alexander Winkler":
We introduce a robust control architecture for the whole-body motion control of torque controlled robots with arms and legs. The method is based on the robust control of contact forces in order to track a planned Center of Mass trajectory. Its appeal lies in the ability to guarantee robust stability and performance despite rigid body model mismatch, actuator dynamics, delays, contact surface stiffness, and unobserved ground profiles. Furthermore, we introduce a task space decomposition approach which removes the coupling effects between contact force controller and the other non-contact controllers. Finally, we verify our control performance on a quadruped robot and compare its performance to a standard inverse dynamics approach on hardware.

* 8 Pages
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In this work we present a trajectory Optimization framework for whole-body motion planning through contacts. We demonstrate how the proposed approach can be applied to automatically discover different gaits and dynamic motions on a quadruped robot. In contrast to most previous methods, we do not pre-specify contact switches, timings, points or gait patterns, but they are a direct outcome of the optimization. Furthermore, we optimize over the entire dynamics of the robot, which enables the optimizer to fully leverage the capabilities of the robot. To illustrate the spectrum of achievable motions, here we show eight different tasks, which would require very different control structures when solved with state-of-the-art methods. Using our trajectory Optimization approach, we are solving each task with a simple, high level cost function and without any changes in the control structure. Furthermore, we fully integrated our approach with the robot's control and estimation framework such that optimization can be run online. By demonstrating a rough manipulation task with multiple dynamic contact switches, we exemplarily show how optimized trajectories and control inputs can be directly applied to hardware.

* Video: https://youtu.be/sILuqJBsyKs
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In this paper we present a new approach for dynamic motion planning for legged robots. We formulate a trajectory optimization problem based on a compact form of the robot dynamics. Such a form is obtained by projecting the rigid body dynamics onto the null space of the Constraint Jacobian. As consequence of the projection, contact forces are removed from the model but their effects are still taken into account. This approach permits to solve the optimal control problem of a floating base constrained multibody system while avoiding the use of an explicit contact model. We use direct transcription to numerically solve the optimization. As the contact forces are not part of the decision variables the size of the resultant discrete mathematical program is reduced and therefore solutions can be obtained in a tractable time. Using a predefined sequence of contact configurations (phases), our approach solves motions where contact switches occur. Transitions between phases are automatically resolved without using a model for switching dynamics. We present results on a hydraulic quadruped robot (HyQ), including single phase (standing, crouching) as well as multiple phase (rearing, diagonal leg balancing and stepping) dynamic motions.

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Optimal and Learning Control for Autonomous Robots has been taught in the Robotics, Systems and Controls Masters at ETH Zurich with the aim to teach optimal control and reinforcement learning for closed loop control problems from a unified point of view. The starting point is the formulation of of an optimal control problem and deriving the different types of solutions and algorithms from there. These lecture notes aim at supporting this unified view with a unified notation wherever possible, and a bit of a translation help to compare the terminology and notation in the different fields. The course assumes basic knowledge of Control Theory, Linear Algebra and Stochastic Calculus.

* Lecture Notes, 101 pages
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This paper combines the fast Zero-Moment-Point (ZMP) approaches that work well in practice with the broader range of capabilities of a Trajectory Optimization formulation, by optimizing over body motion, footholds and Center of Pressure simultaneously. We introduce a vertex-based representation of the support-area constraint, which can treat arbitrarily oriented point-, line-, and area-contacts uniformly. This generalization allows us to create motions such quadrupedal walking, trotting, bounding, pacing, combinations and transitions between these, limping, bipedal walking and push-recovery all with the same approach. This formulation constitutes a minimal representation of the physical laws (unilateral contact forces) and kinematic restrictions (range of motion) in legged locomotion, which allows us to generate various motion in less than a second. We demonstrate the feasibility of the generated motions on a real quadruped robot.

* currently under review for IEEE RA-L
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In this paper, we present an efficient Dynamic Programing framework for optimal planning and control of legged robots. First we formulate this problem as an optimal control problem for switched systems. Then we propose a multi--level optimization approach to find the optimal switching times and the optimal continuous control inputs. Through this scheme, the decomposed optimization can potentially be done more efficiently than the combined approach. Finally, we present a continuous-time constrained LQR algorithm which simultaneously optimizes the feedforward and feedback controller with $O(n)$ time-complexity. In order to validate our approach, we show the performance of our framework on a quadrupedal robot. We choose the Center of Mass dynamics and the full kinematic formulation as the switched system model where the switching times as well as the contact forces and the joint velocities are optimized for different locomotion tasks such as gap crossing, walking and trotting.

* 8 Pages
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This paper studies existing direct transcription methods for trajectory optimization applied to robot motion planning. There are diverse alternatives for the implementation of direct transcription. In this study we analyze the effects of such alternatives when solving a robotics problem. Different parameters such as integration scheme, number of discretization nodes, initialization strategies and complexity of the problem are evaluated. We measure the performance of the methods in terms of computational time, accuracy and quality of the solution. Additionally, we compare two optimization methodologies frequently used to solve the transcribed problem, namely Sequential Quadratic Programming (SQP) and Interior Point Method (IPM). As a benchmark, we solve different motion tasks on an underactuated and non-minimal-phase ball-balancing robot with a 10 dimensional state space and 3 dimensional input space. Additionally, we validate the results on a simulated 3D quadrotor. Finally, as a verification of using direct transcription methods for trajectory optimization on real robots, we present hardware experiments on a motion task including path constraints and actuation limits.

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We present a legged motion planning approach for quadrupedal locomotion over challenging terrain. We decompose the problem into body action planning and footstep planning. We use a lattice representation together with a set of defined body movement primitives for computing a body action plan. The lattice representation allows us to plan versatile movements that ensure feasibility for every possible plan. To this end, we propose a set of rules that define the footstep search regions and footstep sequence given a body action. We use Anytime Repairing A* (ARA*) search that guarantees bounded suboptimal plans. Our main contribution is a planning approach that generates on-line versatile movements. Experimental trials demonstrate the performance of our planning approach in a set of challenging terrain conditions. The terrain information and plans are computed on-line and on-board.

* published 2015
* 7 pages, International Conference on Technologies for Practical Robot Applications
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We present a framework for dynamic quadrupedal locomotion over challenging terrain, where the choice of appropriate footholds is crucial for the success of the behaviour. We build a model of the environment on-line and on-board using an efficient occupancy grid representation. We use Any-time-Repairing A* (ARA*) to search over a tree of possible actions, choose a rough body path and select the locally-best footholds accordingly. We run a n-step lookahead optimization of the body trajectory using a dynamic stability metric, the Zero Moment Point (ZMP), that generates natural dynamic whole-body motions. A combination of floating-base inverse dynamics and virtual model control accurately executes the desired motions on an actively compliant system. Experimental trials show that this framework allows us to traverse terrains at nearly 6 times the speed of our previous work, evaluated over the same set of trials.

* 2015
* 7 pages, IEEE International Conference on Robotics and Automation
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Fluoroscopic X-ray guidance is a cornerstone for percutaneous orthopaedic surgical procedures. However, two-dimensional observations of the three-dimensional anatomy suffer from the effects of projective simplification. Consequently, many X-ray images from various orientations need to be acquired for the surgeon to accurately assess the spatial relations between the patient's anatomy and the surgical tools. In this paper, we present an on-the-fly surgical support system that provides guidance using augmented reality and can be used in quasi-unprepared operating rooms. The proposed system builds upon a multi-modality marker and simultaneous localization and mapping technique to co-calibrate an optical see-through head mounted display to a C-arm fluoroscopy system. Then, annotations on the 2D X-ray images can be rendered as virtual objects in 3D providing surgical guidance. We quantitatively evaluate the components of the proposed system, and finally, design a feasibility study on a semi-anthropomorphic phantom. The accuracy of our system was comparable to the traditional image-guided technique while substantially reducing the number of acquired X-ray images as well as procedure time. Our promising results encourage further research on the interaction between virtual and real objects, that we believe will directly benefit the proposed method. Further, we would like to explore the capabilities of our on-the-fly augmented reality support system in a larger study directed towards common orthopaedic interventions.

* J. Med. Imag. 5(2), 2018
* S. Andress, A. Johnson, M. Unberath, and A. Winkler have contributed equally and are listed in alphabetical order
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