My friends call me Alex. I work at Meta Reality Labs in San Francisco, researching how to move virtual avatars to imitate human movement, e.g. from a Quest headset. This work touches fields like reinforcement learning, motion-tracking and character animation. I got my PhD from ETH Zurich, where I worked on robot motion-planning and trajectory optimization for quadruped robots. This work gave me a solid understanding of the physics of legged locomotion, model-based control and how contacts are used to move floating-base systems. Now that I moved into computer graphics, I'm using my understanding of these physical constraints to synthesize highest quality animations.
Happy to get in touch,
Highlighting some projects here. For videos on all projects, see my Youtube.
Robotics Motion and Path Planning Trajectory Optimization
Legged Locomotion Trajectory Optimization Nonlinear Programming
3 min read
We're used to seeing cars drive around and drones flying over our heads. Why is it much more difficult to make machines walk?
30 min read
To approximate the physics of legged robots mathematically, there exists a variety of models (RBD, Centroidal, SRBD, LIPM). Here we explain their differences and underlying assumptions
10 min read
How to formulate a mathematical problem so it captures the physics of walking? A solution to this problem gives us motions-plans to execute on a robot.
Download pdfs, videos, slides, bibtex info and more. See also Google Scholar.
@inproceedings{10.1145/3550469.3555411, author = {Winkler, Alexander and Won, Jungdam and Ye, Yuting}, title = {QuestSim: Human Motion Tracking from Sparse Sensors with Simulated Avatars}, year = {2022}, isbn = {9781450394703}, publisher = {Association for Computing Machinery}, address = {New York, NY, USA}, url = {https://doi.org/10.1145/3550469.3555411}, doi = {10.1145/3550469.3555411}, booktitle = {SIGGRAPH Asia 2022 Conference Papers}, articleno = {2}, numpages = {8}, keywords = {Reinforcement Learning, Motion Tracking, Character Animation, Wearable Devices}, location = {Daegu, Republic of Korea}, series = {SA '22} }
@inproceedings{10.1145/3550469.3555428, author = {Jiang, Yifeng and Ye, Yuting and Gopinath, Deepak and Won, Jungdam and Winkler, Alexander W. and Liu, C. Karen}, title = {Transformer Inertial Poser: Real-Time Human Motion Reconstruction from Sparse IMUs with Simultaneous Terrain Generation}, year = {2022}, isbn = {9781450394703}, publisher = {Association for Computing Machinery}, address = {New York, NY, USA}, url = {https://doi.org/10.1145/3550469.3555428}, doi = {10.1145/3550469.3555428}, booktitle = {SIGGRAPH Asia 2022 Conference Papers}, articleno = {3}, numpages = {9}, keywords = {Wearable Devices, Human Motion, Inertial Measurement Units}, location = {Daegu, Republic of Korea}, series = {SA '22} }
@article{winkler18, author = {Winkler, Alexander W and Bellicoso, Dario C and Hutter, Marco and Buchli, Jonas}, title = {Gait and Trajectory Optimization for Legged Systems through Phase-based End-Effector Parameterization}, journal = {IEEE Robotics and Automation Letters (RA-L)}, year = {2018}, month = {July}, pages = {1560-1567}, doi = {10.1109/LRA.2018.2798285}, volume = {3}, keywords = {legged locomotion, trajectory optimization} }
@article{winkler17b, author = {Winkler, Alexander W and Farshidian, Farbod and Pardo, Diego and Neunert, Michael and Buchli, Jonas}, title = {Fast Trajectory Optimization for Legged Robots using Vertex-based ZMP Constraints}, journal = {IEEE Robotics and Automation Letters (RA-L)}, year = {2017}, month = {oct}, pages = {2201-2208}, doi = {10.1109/LRA.2017.2723931}, volume = {2}, keywords = {legged locomotion, trajectory optimization} }
@inproceedings{farshidian17b, author = {Farshidian, Farbod and Jelavic, Edo and Winkler, Alexander W and Buchli, Jonas}, title = {Robust Whole-Body Motion Control of Legged Robots}, booktitle = {IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)}, year = {2017}, abstract = {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 noncontact controllers. Finally, we verify our control performance on a quadruped robot and compare its performance to a standard inverse dynamics approach on hardware.} }
@inproceedings{pardo17, author = {Pardo, Diego and Neunert, Michael and Winkler, Alexander W and Grandia, Ruben and Buchli, Jonas}, title = {Hybrid direct collocation and control in the constraint- consistent subspace for dynamic legged robot locomotion}, booktitle = {Robotics, Science and Systems (RSS)}, year = {2017}, abstract = {In this paper, we present an algorithm for optimal planning and control of legged robot locomotion. Given the desired contact sequence, this method generates gaits and dynamic motions for legged robots without resorting to simplified stability criteria. The method uses direct collocation for searching for solutions within the constraint-consistent subspace defined by the robot’s contact configuration. For the differential equation constraints of the collocation algorithm, we use the so-called direct dynamics of a constrained multibody system. The dynamics of a legged robot is different for each contact configuration. Our method deals with such a hybrid nature, and it allows for velocity discontinuities when contacts are made. We introduce the projected impact dynamics constraint to enforce consistency during mode switching. We stabilize the plan using an inverse dynamics controller consistent with the constraints and compatible with the optimal feed-forward control of the motion plan. As a whole, this approach reduces the complexity associated with specifying dynamic motions of a floating-base robot under the constant influence of contact forces. We apply this method on a hydraulically actuated quadruped robot. We show two type of gaits on the physical system (walking and trotting), and other dynamic motions in simulation (jumping and leaping). The results presented here are one of the few examples of an optimal control problem satisfactorily solved and transferred to a real torque-controlled legged robot.}, }
@inproceedings{winkler17a, author = {Winkler, Alexander W and Farshidian, Farbod and Neunert, Michael and Pardo, Diego and Buchli, Jonas}, title = {Online Walking Motion and Foothold Optimization for Quadruped Locomotion}, booktitle = {IEEE International Conference on Robotics and Automation (ICRA)}, year = {2017}, pages = {5308-5313}, doi = {10.1109/ICRA.2017.7989624}, abstract = {We present an algorithm that generates walking motions for quadruped robots without the use of an explicit footstep planner by simultaneously optimizing over both the Center of Mass (CoM) trajectory and the footholds. Feasibility is achieved by imposing stability constraints on the CoM related to the Zero Moment Point and explicitly enforcing kinematic constraints between the footholds and the CoM position. Given a desired goal state, the problem is solved online by a Nonlinear Programming solver to generate the walking motion. Experimental trials show that the algorithm is able to generate walking gaits for multiple steps in milliseconds that can be executed on a real quadruped robot.} }
@inproceedings{farshidian17a, author = {Farshidian, Farbod and Neunert, Michael and Winkler, Alexander W and Rey, Gonzalo and Buchli, Jonas}, title = {An Efficient Optimal Planning and Control Framework For Quadrupedal Locomotion}, booktitle = {IEEE International Conference on Robotics and Automation (ICRA)}, year = {2017}, pages = {93-100}, doi = {10.1109/ICRA.2017.7989016}, abstract = {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.} }
@article{neunert2017, author = {Michael Neunert and Farbod Farshidian and Alexander W. Winkler and Jonas Buchli}, title = {Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds}, journal = {IEEE Robotics and Automation Letters (RA-L)}, year = {2017}, pages = {1502-1509}, volume = {2}, doi = {10.1109/LRA.2017.2665685}, abstract = {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, 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 integrate our approach with the robot’s control and estimation framework such that we are able to run the optimization online. Through several hardware experiments we show that the optimized trajectories and control inputs can be directly applied to physical systems.}, keywords = {Multilegged Robots, Motion and Path Planning, Optimization and Optimal Control} }
@inproceedings{buchli2017, author = {Jonas Buchli and Farbod Farshidian and Alexander W. Winkler and Timothy Sandy and Markus Gifthaler}, title = {Optimal and Learning Control for Autonomous Robots}, booktitle = {arXiv}, year = {2017}, abstract = {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.} }
@article{pardo16, author = {Pardo, Diego and Moeller, Lukas and Neunert, Michael and Winkler, Alexander W. and Buchli, Jonas}, title = {Evaluating direct transcription and nonlinear optimization methods for robot motion planning}, journal = {IEEE Robotics and Automation Letters (RA-L)}, pages = {946-953}, doi = {10.1109/LRA.2016.2527062}, year = {2016}, abstract = {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 solu- tion. Additionally, we compare two optimization methodologies frequently used to solve the transcribed problem, namely Sequen- tial 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.}, keywords = {Optimization and Optimal Control, Underactuated Robots}, }
@inproceedings{winkler15, author = {Winkler, Alexander W. and Mastalli, Carlos and Havoutis, Ioannis and Focchi, Michele and Caldwell, Darwin and Semini, Claudio}, booktitle = {IEEE International Conference on Robotics and Automation (ICRA)}, title = {Planning and Execution of Dynamic Whole-Body Locomotion for a Hydraulic Quadruped on Challenging Terrain}, year = {2015}, pages = {5148-5154}, doi = {10.1109/ICRA.2015.7139916}, abstract = {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.} }
@inproceedings{mastalli2015, author = {Mastalli, Carlos and Havoutis, Ioannis and Winkler, Alexander W. and Caldwell, Darwin and Semini, Claudio}, booktitle = {IEEE International Conference on Practial Robot Applications}, title = {On-line and on-board planning for quadrupedal locomotion, using practical, on-board perception}, year = {2015}, abstract = {We present a legged motion planning approach for quadrupedal locomotion over challenging terrain. We de- compose 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 move ments 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 sub- optimal 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.}, }
@inproceedings{winkler14, author = {Winkler, Alexander W. and Havoutis, Ioannis and Bazeille, Stephane and Ortiz, Jesus and Focchi, Michele and Dillmann, Ruediger and Caldwell, Darwin and Semini, Claudio}, title = {Path planning with force-based foothold adaptation and virtual model control for torque controlled quadruped robots}, booktitle = {IEEE International Conference on Robotics and Automation (ICRA)}, pages = {6476--6482}, year = {2014}, doi = {10.1109/ICRA.2014.6907815}, isbn = {9781479936847}, abstract = {We present a framework for quadrupedal locomotion over highly challenging terrain where the choice of appropriate footholds is crucial for the success of the behaviour. We use a path planning approach which shares many similarities with the results of the DARPA Learning Locomotion challenge and extend it to allow more flexibility and increased robustness. During execution we incorporate an on-line force-based foothold adaptation mechanism that updates the planned motion according to the perceived state of the environment. This way we exploit the active compliance of our system to smoothly interact with the environment, even when this is inaccurately perceived or dynamically changing, and update the planned path on-the-fly. In tandem we use a virtual model controller that provides the feed-forward torques that allow increased accuracy together with highly compliant behaviour on an otherwise naturally very stiff robotic system. We leverage the full set of benefits that a high performance torque controlled quadruped robot can provide and demonstrate the flexibility and robustness of our approach on a set of experimental trials of increasing difficulty.} }
@techreport{winkler13, author = {Winkler, Alexander W.}, title = {Path Planning and Adaptive Execution based on Force-Feedback for Quadruped Locomotion}, institution = {Karlsruhe Institute of Technology and Italian Institute of Technology}, year = {2013}, note = {Masters Thesis}, url_pdf = {mypdfs/13-msc-thesis-winkler.pdf}, }
All code is published on Github.
Welcome to my blog! 🙂 So far a bit philosophy, a bit diary, let's see where it goes.
2019-3-30 · 7 min read
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