Semi-global Exponential Stability for Dual Quaternion Based Rigid-Body Tracking Control

Semi-Global Exponential Stability (SGES) is proved for the combined attitude and position rigid body motion tracking problem, which was previously only known to be asymptotically stable. Dual quaternions are used to jointly represent the rotational and translation tracking error dynamics of the rigid body. A novel nonlinear feedback tracking controller is proposed and a Lyapunov based analysis is provided to prove the semi-global exponential stability of the closed-loop dynamics. Our analysis does not place any restrictions on the reference trajectory or the feedback gains. This stronger SGES result aids in further analyzing the robustness of the rigid body system by establishing Input-to-State Stability (ISS) in the presence of time-varying additive and bounded external disturbances. Motivated by the fact that in many aerospace applications, stringent adherence to safety constraints such as approach path and input constraints is critical for overall mission success, we present a framework for safe control of spacecraft that combines the proposed feedback controller with Control Barrier Functions. Numerical simulations are provided to verify the SGES and ISS results and also showcase the efficacy of the proposed nonlinear feedback controller in several non-trivial scenarios including the Mars Cube One (MarCO) mission, Apollo transposition and docking problem, Starship flip maneuver, collision avoidance of spherical robots, and the rendezvous of SpaceX Dragon 2 with the International Space Station.Comment: 25 page

Decentralized Collaborative Load Transport by Multiple Robots, ICRA

Abstract-With the rapid progress of the robotic technology, it is becoming increasingly common to have multiple robots working together for material transport, cooperative assembly, etc. To ensure the proper handling of the load, especially if it is fragile or needs to be moved rapidly, the constraint force needs to be carefully managed. Tight force coordination is possible if all robots share their force information and the grasp geometry is completely known. When this is not the case, a common approach is to use the leader/follower strategy, where the leader provides the position control for the load and other robots comply based on the individual contact force measurements. This paper considers an alternate decentralized motion and force control method, where all robots participate in the control of the load without sharing any position and force information. Under centralized squeeze force control, robot motion is not affected. However, when the force control is decentralized, a perturbation term is added to the motion control loop. We show that the nominal exponential stability of the motion loop preserves the closed loop stability in the presence of this perturbation. Simulation and experimental results are included to demonstrate the proposed approach

Reactive Control Of Autonomous Dynamical Systems

This thesis mainly consists of five independent papers concerning the reactive control design of autonomous mobile robots in the context of target tracking and cooperative formation keeping with obstacle avoidance in the static/dynamic environment. Technical contents of this thesis are divided into three parts. The first part consists of the first two papers, which consider the target-tracking and obstacle avoidance in the static environment. Especially, in the static environment, a fundamental issue of reactive control design is the local minima problem(LMP) inherent in the potential field methods(PFMs). Through introducing a state-dependent planned goal, the first paper proposes a switching control strategy to tackle this problem. The control law for the planned goal is presented. When trapped into local minima, the robot can escape from local minima by following the planned goal. The proposed control law also takes into account the presence of possible saturation constraints. In addition, a time-varying continuous control law is proposed in the second paper to tackle this problem. Challenges of finding continuous control solutions of LMP are discussed and explicit design strategies are then proposed. The second part of this thesis deals with target-tracking and obstacle avoidance in the dynamic environment. In the third paper, a reactive control design is presented for omnidirectional mobile robots with limited sensor range to track targets while avoiding static and moving obstacles in a dynamically evolving environment. Towards this end, a multiiii objective control problem is formulated and control is synthesized by generating a potential field force for each objective and combining them through analysis and design. Different from standard potential field methods, the composite potential field described in this paper is time-varying and planned to account for moving obstacles and vehicle motion. In order to accommodate a larger class of mobile robots, the fourth paper proposes a reactive control design for unicycle-type mobile robots. With the relative motion among the mobile robot, targets, and obstacles being formulated in polar coordinates, kinematic control laws achieving target-tracking and obstacle avoidance are synthesized using Lyapunov based technique, and more importantly, the proposed control laws also take into account possible kinematic control saturation constraints. The third part of this thesis investigates the cooperative formation control with collision avoidance. In the fifth paper, firstly, the target tracking and collision avoidance problem for a single agent is studied. Instead of directly extending the single agent controls to the multiagents case, the single agent controls are incorporated with the cooperative control design presented in [1]. The proposed decentralized control is reactive, considers the formation feedback and changes in the communication networks. The proposed control is based on a potential field method, its inherent oscillation problem is also studied to improve group transient performance

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

An NMPC-ECBF Framework for Dynamic Motion Planning and Execution in vision-based Human-Robot Collaboration

To enable safe and effective human-robot collaboration (HRC) in smart manufacturing, seamless integration of sensing, cognition, and prediction into the robot controller is critical for real-time awareness, response, and communication inside a heterogeneous environment (robots, humans, and equipment). The proposed approach takes advantage of the prediction capabilities of nonlinear model predictive control (NMPC) to execute a safe path planning based on feedback from a vision system. In order to satisfy the requirement of real-time path planning, an embedded solver based on a penalty method is applied. However, due to tight sampling times NMPC solutions are approximate, and hence the safety of the system cannot be guaranteed. To address this we formulate a novel safety-critical paradigm with an exponential control barrier function (ECBF) used as a safety filter. We also design a simple human-robot collaboration scenario using V-REP to evaluate the performance of the proposed controller and investigate whether integrating human pose prediction can help with safe and efficient collaboration. The robot uses OptiTrack cameras for perception and dynamically generates collision-free trajectories to the predicted target interactive position. Results for a number of different configurations confirm the efficiency of the proposed motion planning and execution framework. It yields a 19.8% reduction in execution time for the HRC task considered

Robust global exponential stabilization on the n-dimensional sphere with applications to trajectory tracking for quadrotors

In this paper, we design a hybrid controller that globally exponentially stabilizes a system evolving on the n-dimensional sphere, denoted by Sn. This hybrid controller is induced by a “synergistic” collection of potential functions on Sn. We propose a particular construction of this class of functions that generates flows along geodesics of the sphere, providing convergence to the desired reference with minimal path length. We show that the proposed strategy is suitable to the exponential stabilization of a quadrotor vehicle