alex.bin — bash — 80x24
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## Research

Robotics Motion and Path Planning 3D Physics/Simulation Legged Locomotion Trajectory Optimization Nonlinear Programming

#### Main contribution

To make a robot move, it needs a motion-plan to follow. Traditionally an engineer examines the terrain and the required task, and then hand-designs how the robot should move. This is tedious, since it requires a custom motion for each situation. My research focussed on automating this by representing the the laws of physics through a single mathematical optimization problem. Off-the-shelf solvers then automatically generate a motion-plan for any terrain or task.... show intro»

3 min overview.

30 minute in-depth explanation.

#### Background knowledge

Optimization-based motion-planning for legged robots connects a lot of different research topics.

##### Why walking is difficult

3 min read  ·  Chapter 1.3

We're used to seeing cars drive around and drones flying over our heads. So why is it is so much more difficult to have machines that walk?

##### Models for legged robots

30 min read  ·  Chapter 1.2

To represent the physics of legged robots mathematically, there exists a variety of models (RBD, Centroidal, SRBD, LIPM). Here we explain their differences and underlying assumptions.

##### Trajectory Optimization

10 min read  ·  Chapter 1.4

To produce a general formulation, we work on a high abstraction layer, defining physical laws in terms of mathematical equations. Existing optimization solvers then solve this problem to produce the motion-plans. Here we present an overview of this type of approach.

#### Game Development with UE4

Personal projects I've been working on using Unreal Engine 4, Blender, Quixel Megascans, Premiere Pro, etc.

For videos on all projects, checkout my Youtube channel.

## Software

All code is published on my Github. The approach described in the above paper is implemented by `towr`, which uses the NLP solver interface `ifopt` to formulate the problem independent of the solver. The ROS package `xpp` is used to visualize motions.

Light-weight and extensible C++ library for trajectory optimization for legged robots.

Eigen-based, light-weight C++ Interface to NLP Solvers (Ipopt, Snopt).

Visualization of legged robots, forces, support areas, ZMP, CoM etc. in ROS rviz.

## Publication List

Optimization-based motion planning for legged robots. Winkler, A. W Ph.D. Thesis, ETH Zurich. 2018
```@phdthesis{winkler18_phd,
author    = {Winkler, Alexander W},
title     = {Optimization-based motion planning for legged robots},
publisher = {ETH Zurich},
year      = {2018},
school    = {ETH Zurich},
doi       = {10.3929/ethz-b-000272432},
abstract  = {What are the most prominent physical restrictions that make legged locomotion difficult?
Which dynamic models (RBD, Centroidal, SRBD, LIPM) can be used to
capture the physics of legged locomotion and what is the trade-off between them?
How can Trajectory Optimization help to generate universal solutions?
What criteria can be used to compare motion planning algorithms?
How to use the SRBD to optimize for the full 6D-base, end-effectors and gait
in milliseconds?.}
}

```
What are the most prominent physical restrictions that make legged locomotion difficult? Which dynamic models (RBD, Centroidal, SRBD, LIPM) can be used to capture the physics of legged locomotion and what is the trade-off between them? How can Trajectory Optimization help to generate universal solutions? What criteria can be used to compare motion planning algorithms? How to use the SRBD to optimize for the full 6D-base, end-effectors and gait in milliseconds?.
Gait and Trajectory Optimization for Legged Systems through Phase-based End-Effector Parameterization. Winkler, A. W; Bellicoso, D. C; Hutter, M.; and Buchli, J. IEEE Robotics and Automation Letters (RA-L). 2018
```@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},
abstract  = {We present a single Trajectory Optimization formulation
for legged locomotion that automatically determines
the gait-sequence, step-timings, footholds, swing-leg motions and
6D body motion over non-flat terrain, without any additional
modules. Our phase-based parameterization of feet motion and
forces allows to optimize over the discrete gait sequence using
only continuous decision variables. The system is represented
using a simplified Centroidal dynamics model that is influenced
by the feet’s location and forces. We explicitly enforce friction
cone constraints, depending on the shape of the terrain. The
NLP solver generates highly dynamic motion-plans with full
flight-phases for a variety of legged systems with arbitrary
morphologies in an efficient manner. We validate the feasibility
of the generated plans in simulation and on the real quadruped
robot ANYmal. Additionally, the entire solver software TOWR
used to generate these motions is made freely available.},
keywords  = {legged locomotion, trajectory optimization}
}

```
We present a single Trajectory Optimization formulation for legged locomotion that automatically determines the gait-sequence, step-timings, footholds, swing-leg motions and 6D body motion over non-flat terrain, without any additional modules. Our phase-based parameterization of feet motion and forces allows to optimize over the discrete gait sequence using only continuous decision variables. The system is represented using a simplified Centroidal dynamics model that is influenced by the feet’s location and forces. We explicitly enforce friction cone constraints, depending on the shape of the terrain. The NLP solver generates highly dynamic motion-plans with full flight-phases for a variety of legged systems with arbitrary morphologies in an efficient manner. We validate the feasibility of the generated plans in simulation and on the real quadruped robot ANYmal. Additionally, the entire solver software TOWR used to generate these motions is made freely available.
Fast Trajectory Optimization for Legged Robots using Vertex-based ZMP Constraints. Winkler, A. W; Farshidian, F.; Pardo, D.; Neunert, M.; and Buchli, J. IEEE Robotics and Automation Letters (RA-L). 2017
```@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},
abstract  = {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
keywords  = {legged locomotion, trajectory optimization}
}

```
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.
Robust Whole-Body Motion Control of Legged Robots. Farshidian, F.; Jelavic, E.; Winkler, A. W; and Buchli, J. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). 2017
```@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.}
}

```
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.
Hybrid direct collocation and control in the constraint- consistent subspace for dynamic legged robot locomotion. Pardo, D.; Neunert, M.; Winkler, A. W; Grandia, R.; and Buchli, J. In Robotics, Science and Systems (RSS). 2017
```@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.},
}

```
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.
Online Walking Motion and Foothold Optimization for Quadruped Locomotion. Winkler, A. W; Farshidian, F.; Neunert, M.; Pardo, D.; and Buchli, J. In IEEE International Conference on Robotics and Automation (ICRA). 2017
```@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
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.}
}

```
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.
An Efficient Optimal Planning and Control Framework For Quadrupedal Locomotion. Farshidian, F.; Neunert, M.; Winkler, A. W; Rey, G.; and Buchli, J. In IEEE International Conference on Robotics and Automation (ICRA). 2017
```@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
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.}
}

```
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.
Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds. Neunert, M.; Farshidian, F.; Winkler, A. W.; and Buchli, J. IEEE Robotics and Automation Letters (RA-L). 2017
```@article{neunert2017,
author    = {Michael Neunert and
Farbod Farshidian and
Alexander W. Winkler and
Jonas Buchli},
title     = {Trajectory Optimization Through Contacts and
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}
}

```
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.
Optimal and Learning Control for Autonomous Robots. Buchli, J.; Farshidian, F.; Winkler, A. W.; Sandy, T.; and Gifthaler, M. In arXiv. 2017
```@inproceedings{buchli2017,
author    = {Jonas Buchli and
Farbod Farshidian and
Alexander W. Winkler and
Timothy Sandy and
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.}
}

```
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.
Evaluating direct transcription and nonlinear optimization methods for robot motion planning. Pardo, D.; Moeller, L.; Neunert, M.; Winkler, A. W.; and Buchli, J. IEEE Robotics and Automation Letters (RA-L). 2016
```@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.
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},
}

```
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.
Planning and Execution of Dynamic Whole-Body Locomotion for a Hydraulic Quadruped on Challenging Terrain. Winkler, A. W.; Mastalli, C.; Havoutis, I.; Focchi, M.; Caldwell, D.; and Semini, C. In IEEE International Conference on Robotics and Automation (ICRA). 2015
```@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.}
}

```
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.
On-line and on-board planning for quadrupedal locomotion, using practical, on-board perception. Mastalli, C.; Havoutis, I.; Winkler, A. W.; Caldwell, D.; and Semini, C. In IEEE International Conference on Practial Robot Applications. 2015
```@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.},
}

```
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.
Path planning with force-based foothold adaptation and virtual model control for torque controlled quadruped robots. Winkler, A. W.; Havoutis, I.; Bazeille, S.; Ortiz, J.; Focchi, M.; Dillmann, R.; Caldwell, D.; and Semini, C. In IEEE International Conference on Robotics and Automation (ICRA). 2014
```@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
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.}
}

```
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.
Path Planning and Adaptive Execution based on Force-Feedback for Quadruped Locomotion. Winkler, A. W. Technical Report Karlsruhe Institute of Technology and Italian Institute of Technology. Masters Thesis, 2013
```@techreport{winkler13,
author      = {Winkler, Alexander W.},
title       = {Path Planning and Adaptive Execution based on Force-Feedback
institution = {Karlsruhe Institute of Technology and
Italian Institute of Technology},
year        = {2013},
note        = {Masters Thesis},
url_pdf     = {mypdfs/13-msc-thesis-winkler.pdf},
}

```
Implementation of a Software-Agent to Control a Microgripper in a Dezentralized Manner. Winkler, A. W. Technical Report Karlsruhe Institute of Technology. Bachelors Thesis, 2012.
```@techreport{winkler12,
author      = {Winkler, Alexander W.},
title       = {Implementation of a Software-Agent to Control
a Microgripper in a Dezentralized Manner},
institution = {Karlsruhe Institute of Technology},
year        = {2012},
note        = {Bachelors Thesis},
}
```

## Blog

Welcome to my blog! 🙂 So far a bit philosophy, a bit diary, let's see where it goes.

#### Six months backpacking

###### and mastering the Bum Gun

I am sitting on the toilet throwing my shit-stained toilet paper in the trash can under the sink whe... read more

#### Collect memories or things?

###### Why they're not so different

It's Christmas Eve and I'm waiting for my plane at LAX scrolling through my Instagram feed. An image ... read more

#### Living like a Buddhist monk

###### 10 days of silent meditation

My ass hurt, my concentration was gone and time seemed to stand still. I squinted open my eyes just e... read more