10/26/2023
By Danielle Fretwell

The Francis College of Engineering, Department of Mechanical Engineering, invites you to attend a Doctoral Dissertation defense by Amir Iqbal on "Modeling, Planning, and Control of Legged Locomotion on Dynamic Rigid Surfaces."

Candidate Name: Amir Iqbal
Degree: Doctoral
Defense Date: Thursday, Nov. 9, 2023
Time: 9 to 11 a.m. EDT
Location: Dandeneau Hall 214


Committee

  • Advisor: Christopher Niezrecki, Ph.D., Distinguished University Professor, Mechanical Engineering, UML
  • Yan Gu, Ph. D., Associate Professor, Mechanical Engineering, Purdue University
  • Kshitij Jerath, Ph. D., Assistant Professor, Mechanical Engineering, UML
  • Kelilah Wolkowicz, Ph. D., Assistant Professor, Mechanical Engineering, UML
  • Sushant Veer, Ph. D., Senior Research Scientist, NVIDIA Research

Brief Abstract:
Legged robots move around by using their legs to make and break contact with the ground. Thanks to this unique form of locomotion, legged robots have the great potential to navigate over difficult terrains and assist humans in performing demanding tasks in hazardous environments. However, the existing approaches of dynamic modeling, motion planning, and control design do not explicitly address the challenges of legged locomotion on dynamic rigid surfaces (i.e., rigid surfaces that move in the inertial frame). This dissertation aims to bridge the existing knowledge gaps in the modeling, planning, and control of legged robot locomotion on dynamic rigid surfaces (DRSes). To achieve the overarching goal, this dissertation comprises the following three main studies.

The first study derives a full-order dynamic model of legged walking on a DRS, proposes a provably stabilizing controller, and validates the modeling and control framework in simulations and hardware experiments. The control approach is synthesized based on the formulation of the full-order robot model as a hybrid, time-varying system. The stability analysis of the closed-loop control system is performed through the construction of multiple Lyapunov functions. The validation results in simulations and hardware experiments confirm the effectiveness of the proposed control approach in guaranteeing the stability and robustness of a quadrupedal robot walking on a DRS with known periodic motion. Still, this study relies on computationally expensive offline trajectory planning, which is unsuitable for real-world applications where frequent replanning is typically demanded to ensure locomotion robustness under uncertainties. To that end, the subsequent contributions aim to realize efficient trajectory planning for real-time applications.

The second study derives a reduced-order dynamic model of legged walking on a DRS and introduces an approximate analytical solution to the model under a vertical sinusoidal DRS motion (e.g., ship motion in regular sea waves). Furthermore, the study designs a hierarchical planner that exploits the proposed analytical solution to enable real-time, physically feasible motion generation for locomotion on a DRS. The validation results support the efficiency and accuracy of the proposed solution in simulations, as well as the efficiency and physical feasibility of the proposed planner through 3-D realistic simulations and hardware experiments. Yet, this framework only solves the real-time locomotion planning problem for a DRS with a sinusoidal vertical movement, which may not be suitable for DRSes with general motions. To overcome this limitation, the last focus of this dissertation research is on legged locomotion under an unknown general (periodic or aperiodic) vertical DRS movement.

The final study of this dissertation presents a hierarchical control framework to enable robust legged locomotion on DRSes with general unknown vertical motions. The key novelty of the framework lies in its higher layer, which is a discrete-time, robustly stabilizing footstep controller. The footstep controller is based on a new hybrid time-varying linear inverted pendulum (HT-LIP) model for capturing essential DRS locomotion dynamics and incorporates a new set of stability conditions to ensure robust stability under uncertain vertical DRS motions. Further, the footstep controller is cast as a quadratic program, integrating the proposed HT-LIP model and essential stability conditions. The middle layer of the framework takes the desired footstep locations as input to produce kinematically feasible whole-body reference trajectories, which are then accurately tracked by a lower-layer full-body torque controller. Hardware experiments on a Unitree Go1 quadrupedal robot confirm the robustness of the proposed framework under various general vertical DRS motions and uncertainties (e.g., slippery and uneven surfaces, external load, unknown sway mot).