Li, Zhibin

Vijayakumar, Sethu

Chatzinikolaidis, Iordanis

Engineering and Physical Sciences Research Council (EPSRC)

2022-01-10T14:12:54Z

2022-01-10T14:12:54Z

2021-11-30

For legged robots, generating dynamic and versatile motions is essential for interacting with complex and ever-changing environments. So far, robots that routinely operate reliably over rough terrains remains an elusive goal. Yet the primary promise of legged locomotion is to replace humans and animals in performing tedious and menial tasks, without requiring changes in the environment as wheeled robots do. A necessary step towards this goal is to endow robots with capabilities to reason about contacts but this vital skill is currently missing. An important justification for this is that contact phenomena are inherently non-smooth and non-convex. As a result, posing and solving problems involving contacts is non-trivial. Optimization-based motion planning constitutes a powerful paradigm to this end. Consequently, this thesis considers the problem of generating motions in contact-rich situations. Specifically, we introduce several methods that compute dynamic and versatile motion plans from a holistic optimization perspective based on trajectory optimization techniques. The advantage is that the user needs to provide a high-level task description in the form of an objective function only. Subsequently, the methods output a detailed motion plan—that includes contact locations, timings, gait patterns—that optimally achieves the high-level task. Initially, we assume that such a motion plan is available, and we investigate the relevant control problem. The problem is to track a nominal motion plan as close as possible given external disturbances by computing inputs for the robot. Thus, this stage typically follows the motion planning stage. Additionally, this thesis presents methods that do not necessarily require a separate control stage by computing the controller structure automatically. Afterwards, we proceed to the main parts of this thesis. First, assuming a pre-specified contact sequence, we formulate a trajectory optimization method reminiscent of hybrid approaches. Its backbone is a high-accuracy integrator, enabling reliable long-term motion planning while satisfying both translational and rotational dynamics. We utilize it to compute motion plans for a hopper traversing rough terrains—with gaps and obstacles—and performing explosive motions, like a somersault. Subsequently, we provide a discussion on how to extend the method when the contact sequence is unspecified. In the next chapter, we increase the complexity of the problem in many aspects. First, we formulate the problem in joint-level utilizing full dynamics and kinematics models. Second, we assume a contact-implicit perspective, i.e. decisions about contacts are implicitly defined in the problem’s formulation rather than defined as explicit contact modes. As a result, pre-specification of the contact interactions is not required, like the order by which the feet contact the ground for a quadruped robot model and the respective timings. Finally, we extend the classical rigid contact model to surfaces with soft and slippery properties. We quantitatively evaluate our proposed framework by performing comparisons against the rigid model and an alternative contact-implicit framework. Furthermore, we compute motion plans for a high-dimensional quadruped robot in a variety of terrains exhibiting the enhanced properties. In the final study, we extend the classical Differential Dynamic Programming algorithm to handle systems defined by implicit dynamics. While this can be of interest in its own right, our particular application is computing motion plans in contact-rich settings. Compared to the method presented in the previous chapter, this formulation enables experiencing contacts with all body parts in a receding horizon fashion, albeit with limited contact discovery capabilities. We demonstrate the properties of our proposed extension by comparing implicit and explicit models and generating motion plans for a single-legged robot with multiple contacts both for trajectory optimization and receding horizon settings. We conclude this thesis by providing insights and limitations of the proposed methods, and possible future directions that can improve and extend aspects of the presented work.

https://hdl.handle.net/1842/38388

http://dx.doi.org/10.7488/era/1653

en

The University of Edinburgh

I. Chatzinikolaidis and Z. Li (2021). “Trajectory optimization of contact-rich motions using implicit differential dynamic programming”. In: IEEE Robotics and Automation Letters. Vol. 6. 2, pp. 2626–2633. doi: 10.1109/LRA.2021. 3061341

I. Chatzinikolaidis, Y. You, and Z. Li (2020). “Contact-implicit trajectory optimization using an analytically solvable contact model for locomotion on variable ground”. In: IEEE Robotics and Automation Letters 5.4, pp. 6357–6364. doi: 10.1109/LRA.2020.3010754.

I. Chatzinikolaidis, T. Stouraitis, S. Vijayakumar, and Z. Li (2018). “Nonlinear optimization using discrete variational mechanics for dynamic maneuvers of a 3D one-leg hopper”. In: Proc. IEEE International Conference on Humanoid Robots, pp. 932–937. doi: 10.1109/HUMANOIDS.2018.8624981.

T. Stouraitis, I. Chatzinikolaidis, M. Gienger, and S. Vijayakumar (2020). “Online hybrid motion planning for dyadic collaborative manipulation via bilevel optimization”. In: IEEE Transactions on Robotics 36.5, pp. 1452–1471. doi: 10. 1109/TRO.2020.2992987

J. Wang, I. Chatzinikolaidis, C. Mastalli, W. Wolfslag, G. Xin, S. Tonneau, and S. Vijayakumar (2020). “Automatic gait pattern selection for legged robots”. In: Proc. IEEE International Conference on Intelligent Robots and Systems, pp. 3990–3997. doi: 10.1109/IROS45743.2020.9340789

K. Yuan, I. Chatzinikolaidis, and Z. Li (2019). “Bayesian optimization for whole-body control of high-degree-of-freedom robots through reduction of di mensionality”. In: IEEE Robotics and Automation Letters 4.3, pp. 2268–2275. doi: 10.1109/LRA.2019.2901308.

W. Hu, I. Chatzinikolaidis, K. Yuan, and Z. Li (2018). “Comparison study of nonlinear optimization of step durations and foot placement for dynamic walking”. In: Proc. IEEE International Conference on Robotics and Automation, pp. 433–439. doi: 10.1109/ICRA.2018.8461101.

T. Stouraitis, I. Chatzinikolaidis, M. Gienger, and S. Vijayakumar (2018). “Dyadic collaborative manipulation through hybrid trajectory optimization”. In: Conference on Robot Learning (CoRL). Vol. 87, pp. 869–878. url: http: / / proceedings . mlr . press / v87 / stouraitis18a . html

Q. Li, I. Chatzinikolaidis, Y. Yang, S. Vijayakumar, and Z. Li (2017). “Robust foot placement control for dynamic walking using online parameter estimation”. In: Proc. IEEE International Conference on Humanoid Robots, pp. 165–170. doi: 10.1109/HUMANOIDS.2017.8239552

legged robots

legged locomotion

motion planning

numerical optimization viewpoint

trajectory optimization methods

high-accuracy integrator

contact-implicit perspective

Differential Dynamic Programming

Optimization-based multi-contact motion planning for legged robots

Thesis or Dissertation

Doctoral

PhD Doctor of Philosophy