# Robust Optimization-Based Control and Planning for Legged Robots

### ICRA 2016 Workshop - Room A1

### May 16th

During the last 10 years the field of legged robots has been strongly influenced by the advent of efficient optimization techniques, which coupled with cheap and fast computers have allowed for the resolution of optimization problems inside high-frequency control loop. However, despite these recent advances, the results of the Darpa Robotics Challenge finals (June 2015) have clearly shown the lack of robustness of these control/planning algorithms: unmodeled uncertainties have often been the cause of failures.

This workshop aims to understand whether robust optimization could be the right tool to account for the countless uncertainties affecting legged robots, such as modeling errors, actuation inaccuracies, estimation uncertainties and delays. Bringing together people working on robust optimization, robust Model Predictive Control, and legged robots, we will try to answer to questions such as:

- What limits us in transferring from simulations to real robots? Is it modeling assumptions / bandwidth / uncertainty?
- Is robust optimization fast enough for application in control?
- Can improved robustness outweigh slower control rates?
- How to model and identify uncertainties?
- Which uncertainties are the most important to take into account?
- Are there modeling assumptions that make computation hard, but are not so important on real systems?

## Topics of the workshop

- robust model predictive control
- robust optimization
- optimization-based control
- whole-body control
- real-robot implementations

## Organizers

- Andrea Del Prete, LAAS/CNRS, France
- Russ Tedrake, MIT, USA
- Alexander Herzog, Max Planck IS, Germany
- The workshop is supported by the IEEE/RAS Technical Committees on Model-Based Optimization for Robotics and Whole-Body Control

## Invited Speakers

The workshop schedule can be downloaded here.**Introduction**

**Andrea Del Prete**(LAAS/CNRS) - slides

**Boris Houska**(ShanghaiTech University) - slides

**Melanie Zeilinger**(ETH) - slides

The first part of the talk will provide an introduction to robust MPC, where we will review the main method classes and discuss the central underlying technique of constraint tightening. Questions of computation and robustness in real-time environments will be addressed. The second part of the talk will focus on the challenge of characterizing uncertainties and the impact on closed-loop performance. We will present some of our recent results on improving performance and robustness by identifying uncertainties online and show techniques for maintaining the desired theoretical properties when the design assumptions on uncertainties are violated.

**References:**

E. D. Klenske, M. N. Zeilinger, B. Schölkopf and P. Hennig. *Gaussian Process-Based Predictive Control for Periodic Error Correction.* IEEE Transactions on Control Systems Technology, (2016)

A. K. Akametalu, J. F. Fisac, J. H. Gillula, S. Kaynama, M. N. Zeilinger and C. J. Tomlin. *Reachability-based safe learning with Gaussian processes.* IEEE Conference on Decision and Control, (2014)

M. N. Zeilinger, M. Morari and C. N. Jones. *Soft Constrained Model Predictive Control With Robust Stability Guarantees.* IEEE Transactions on Automatic Control, (2014)

**Francesco Nori**(IIT) - slides

**Richard Oberdieck**(Texas A&M University) - slides

In this presentation, we will first provide a historical progress report of the key developments in multi-parametric programming and control along with recent theoretical and algorithmic advances in explicit robust multi-parametric programming and control for discrete and continuous linear, quadratic and mixed integer systems. We will also present an overview of PAROC, a prototype software system which allows for the representation, modelling and solution of integrated scheduling and control problems. Its main features include: (i) a high-fidelity dynamic model representation, also involving global sensitivity analysis, parameter estimation and mixed integer dynamic optimization capabilities; (ii) a suite/toolbox of model approximation methods; (iii) a host of multi-parametric programming solvers for mixed continuous/integer problems; (iv) a state-space modelling representation capability for scheduling and control problems; and (v) an advanced control toolkit for robust multi-parametric/explicit MPC and moving horizon reactive scheduling problems. Algorithms that enable the integration capabilities of the systems for design, scheduling and control are presented along with applications in sustainable energy systems, smart manufacturing and personalized healthcare engineering.

**References:**

Pistikopoulos, E. N.; Diangelakis, N. A.; Oberdieck, R.; Papathanasiou, M. M.; Nascu, I.; Sun, M. *PAROC - an Integrated Framework and Software Platform for the Optimization and Advanced Model-Based Control of Process Systems.* Chemical Engineering Science, (2015)

Bemporad, A.; Morari, M.; Dua, V.; Pistikopoulos, E. N. *The explicit quadratic regulator for constrained systems.* Automatica, (2002)

Oberdieck, R.; Pistikopoulos, E. N. *Explicit hybrid model-predictive control: The exact solution.* Automatica, (2015)

Kouramas, K. I.; Panos, C.; Faisca, N. P.; Pistikopoulos, E. N. *An algorithm for robust explicit/multi-parametric model predictive control.* Automatica, (2013)

**Ludovic Righetti**(MPI) - slides

**References:**

Alexander Herzog, Nicholas Rotella, Sean Mason, Felix Grimminger, Stefan Schaal, Ludovic Righetti. *Momentum Control with Hierarchical Inverse Dynamics on
a Torque-Controlled Humanoid.* Autonomous Robots, 2015.

Alexander Herzog, Nicholas Rotella, Stefan Schaal, Ludovic Righetti. *Trajectory generation for multi-contact momentum-control.* Humanoids, 2015.

Alexander Herzog, Stefan Schaal, Ludovic Righetti. *Structured contact force optimization for kino-dynamic motion generation.* arXiv:1605.08571, 2016.

Nicholas Rotella, Michael Bloesch, Ludovic Righetti, Stefan Schaal. *State Estimation for a Humanoid Robot .* IROS, 2014.

Nicholas Rotella, Alexander Herzog, Stefan Schaal, Ludovic Righetti. *Humanoid Momentum Estimation Using Sensed Contact
Wrenches.* Humanoids, 2015.

Brahayam Ponton, Stefan Schaal, Ludovic Righetti. *Risk sensitive nonlinear optimal control with
measurement uncertainty.* arXiv:1605.04344, 2016.

**Emo Todorov**(University of Washington)

**Salman Faraji**(EPFL) - slides

**Kris Hauser**(Duke University)

**Didier Henrion**(LAAS/CNRS) - slides

**References:**

**Michael Posa**(MIT) - slides

**References:**

Michael Posa, Mark Tobenkin, and Russ Tedrake. *Stability Analysis and Control of Rigid-Body Systems with Impacts and Friction.* To appear in the IEEE Transactions on Control (TAC), 2016.

Michael Posa, Mark Tobenkin, and Russ Tedrake. *Lyapunov analysis of rigid body systems with impacts and friction via sums-of-squares.* Intl. Conf. on Hybrid Systems: Computation and Control (HSCC), 2013.

**Amir Ali Ahmadi**(Princeton University)