Projects

Feedback control design near contact surfaces

When executing a desired motion, robotic controllers remain largely unable to adapt to unexpected contact events. Similarly, they are unable to leverage the potential benefits that could arise from initiating contact, such as bracing against a wall. A local control policy that, in real-time, can adaptively select from a number of potential contacts will enable safer and more capable robots. A fundamental challenge lies in the complexity of the contacts between robot and object. Frictional contact introduces a host of mathematical challenges to the governing equations of motion, particularly discontinuities which result in a combinatorial number of hybrid modes. While current robots must operate with extreme caution, fearful of unexpected contact, research into fundamental control strategies will enable high-performance robots to fluidly and robustly interact with the world. This project will combine theoretical analysis with experimentation on grasping and dexterous manipulation.


 

Related publications

Alp Aydinoglu, Victor Preciado, Michael Posa

Contact-Aware Controller Design for Complementarity Systems

Under review, 2019.

Abstract | Links | BibTeX

Michael Posa, Mark Tobenkin, Russ Tedrake

Stability analysis and control of rigid-body systems with impacts and friction

IEEE Transactions on Automatic Control (TAC), 61 (6), pp. 1423–1437, 2016.

Abstract | Links | BibTeX

Michael Posa, Mark Tobenkin, Russ Tedrake

Lyapunov analysis of rigid body systems with impacts and friction via sums-of-squares

The 16th International Conference on Hybrid Systems: Computation and Control (HSCC), pp. 63–72, ACM 2013, (Winner of the Best Paper Award).

Abstract | Links | BibTeX


 

Formal methods for robust legged locomotion

Legged robots, bipedal or otherwise, promise the capability to traverse complex indoor and outdoor environments. Despite recent success, most control strategies either require precise footfalls or have been carefully hand-designed. Our aim is to research contact-robust locomotion and design algorithms which, given a robot specification and objective, can design efficient and stable motions over challenging terrain. One aspect to this research is to investigate “mid-level” dynamic models of walking robots, models that expose the relevant centroidal dynamics without the unnecessary complexity of full rigid-body descriptions. A mathematically rigorous approach to these problems, utilizing computation and numerical optimization, will be more extensible to new robots and tasks, and ultimately an enabling technology for legged robots to leave research settings. As part of this project, we will combine simulated experiments with laboratory testing on an Agility Robotics Cassie bipedal robot.

Related publications

Yu-Ming Chen, Michael Posa

Optimal Reduced-order Modeling of Bipedal Locomotion

Under review, 2019.

Abstract | Links | BibTeX

Michael Posa, Twan Koolen, Russ Tedrake

Balancing and Step Recovery Capturability via Sums-of-Squares Optimization

Robotics: Science and Systems (RSS), 2017.

Abstract | Links | BibTeX

Twan Koolen, Michael Posa, Russ Tedrake

Balance control using center of mass height variation: limitations imposed by unilateral contact

2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids), pp. 8–15, IEEE, 2016, (Finalist for the Best Oral Paper Award).

Abstract | Links | BibTeX


Modeling of multi-contact motion

At a fundamental level, multi-contact motion is inherently ill-conditioned. Think, for example, of a four-legged table or a block of wood falling end-first onto the ground. These motions are not only hybrid, but they betray extreme sensitivity to initial conditions. We are interested in describing multi-contact motion on a number of fundamental levels. Can, via basic principles and experimental data, these motions be predicted? When, as in the case of the chaotic bouncing block, reliable prediction is impossible, can we identify and understand this phenomena? In particular, we aim to exploit the structure of both dynamic and quasi-static notions of non-smooth dynamics. This active project incorporates elements of optimization-based modeling, formal analysis, and machine learning.

Related publications

Mathew Halm, Michael Posa

Modeling and Analysis of Non-unique Behaviors in Multiple Frictional Impacts

Robotics: Science and Systems (RSS), 2019.

Abstract | Links | BibTeX

Mathew Halm, Michael Posa

A Quasi-static Model and Simulation Approach for Pushing, Grasping, and Jamming

The Workshop on the Algorithmic Foundations of Robotics (WAFR), 2018.

Abstract | Links | BibTeX


Multi-contact trajectory optimization

Trajectory optimization algorithms utilize nonlinear programming to synthesize locally optimal motions for high-dimensional systems with potentially complex sets of goals and constraints. Our research in this area is targeted toward optimization in contact-rich environments, where the exact sequence of contacts and impacts needed for a motion is initially unknown. Given some number of rigid links or points on the robot which might contact the environment, there are exponentially many possible contact states. For scenarios of even modest complexity, it is computationally intractable to optimize over all such states and sequences. Research into contact-implicit optimization directly incorporates the complementarity structure of contact dynamics, and is capable of reasoning over possible contact sequences  explicit enumeration. Additional work has focused on refining and tracking these contact-rich motions by appropriately reasoning about the geometric manifold induced by contact.


 

Related publications

Michael Posa, Scott Kuindersma, Russ Tedrake

Optimization and Stabilization of Trajectories for Constrained Dynamical Systems

International Conference on Robotics and Automation (ICRA), 2016.

Abstract | Links | BibTeX

Michael Posa, Cecilia Cantu, Russ Tedrake

A direct method for trajectory optimization of rigid bodies through contact

The International Journal of Robotics Research (IJRR), 33 (1), pp. 69–81, 2014.

Abstract | Links | BibTeX

Michael Posa, Russ Tedrake

Direct Trajectory Optimization of Rigid Body Dynamical Systems Through Contact

The Workshop on the Algorithmic Foundations of Robotics (WAFR), pp. 16, Cambridge, MA, 2012.

Abstract | Links | BibTeX