Committee:

Dr. Seth Hutchinson, ECE, Chair, Advisor

Dr. Sam Coogan, ECE

Dr. Ye Zhao, ME

Dr. Ousama Khatib, Stanford

Dr. Kyriakos Vamvoudakis, AE

Dr. Magnus Egerstedt, ECE

Abstract: apunov function and control barrier functions in the operational space and solved as a Quadratic Programming (QP) problem. In order to ensure real-time computation while satisfying constraints with highly coupled dynamics, we design control barriers using higher-order ellipsoids for both the task and joint constraints. This reduces the number of constraints and provides a unified framework to meet multiple objectives while ensuring exponential convergence, where applicable, and minimum-norm control in a real-time setting. We also ensure singularity avoidance by using the manipulability index and the corresponding manipulability jacobian. We also discuss the formulation to ensure safety only while utilizing any nominal controller. We apply our framework on seven degrees of freedom Kuka iiwa LBR robotic manipulator with two task constraints, two joint constraints, and one torque constraint while ensuring that manipulator is never in any singular configuration on the drake physic simulator and hardware, and the results are compared with weighted QP optimization. We then extend the formulation to the consensus problem in operational space for the heterogeneous robotic manipulator, with each manipulator satisfying its task and joint constraint while achieving consensus. Finally, we extend the formulation to wheel inverted pendulum humanoid and verify it on simulation using the Dynamic Animation and Robotics Toolkit (DART) physics engine.