Trajectory Generation for a Multibody Robotic System: Modern Methods Based on Product of Exponentials

This work presents several trajectory generation algorithms for multibody robotic systems based on the Product of Exponentials (PoE) formulation, also known as screw theory. A PoE formulation is first developed to model the kinematics and dynamics of a multibody robotic manipulator (Sawyer Robot) with 7 revolute joints and an end-effector. In the first method, an Inverse Kinematics (IK) algorithm based on the Newton-Raphson iterative method is applied to generate constrained joint-space trajectories corresponding to straight-line and curvilinear motions of the end effector in Cartesian space with finite jerk. The second approach describes Constant Screw Axis (CSA) trajectories which are generated using Machine Learning (ML) and Artificial Neural Networks (ANNs) techniques. The CSA method smooths the trajectory in the Special Euclidean (SE(3)) space. In the third approach, a multi-objective Swarm Intelligence (SI) trajectory generation algorithm is developed, where the IK problem is tackled using a combined SI-PoE ML technique resulting in a joint trajectory that avoids obstacles in the workspace, and satisfies the finite jerk constraint on end-effector while minimizing the torque profiles. The final method is a different approach to solving the IK problem using the Deep Q-Learning (DQN) Reinforcement Learning (RL) algorithm which can generate different joint space trajectories given the Cartesian end-effector path. For all methods above, the Newton-Euler recursive algorithm is implemented to compute the inverse dynamics, which generates the joint torques profiles. The simulated torque profiles are experimentally validated by feeding the generated joint trajectories to the Sawyer robotic arm through the developed Robot Operating System (ROS) - Python environment in the Software Development Kit (SDK) mode. The developed algorithms can be used to generate various trajectories for robotic arms (e.g. spacecraft servicing missions)

Experimental and Computational Analysis of a 3D Printed Wing Structure

Correct prediction of aeroelastic response is a crucial part in designing flutter or divergence free aircrafts within a designated flight envelope. The aeroelastic analysis includes specifically tailoring the design in order to prevent flutter (passive control) or eliminate it by applying input on control surfaces (active control). High-fidelity models such as coupled Computational Fluid Dynamics (CFD) - Computational Structural Dynamics (CSD) can obtain full structural and aerodynamic behavior of a deformable aircraft. However, these models are so large that pose a significant challenge from the control systems design perspective. Thus, the development of an aeroelastic modeling software that can be used for further control design is the main motivation of this thesis. In addition, an aeroelastic analysis of a topologically optimized wing geometry will serve as a validation tool of the software. Initially, a 3D printed prototype of the wing is validated against static deformation tests as well as dynamic Ground Vibration Tests (GVT). The developed model is compared against the commercial software Nastran/Patran. Further plans include experimental aerodynamic test of 3D printed wing in the new Embry-Riddle Aeronautical University’s (ERAU) wind tunnel to validate the proposed model

Synthesis, Analysis, Design and Manufacturing of an Upper-Limb Rehabilitation Apparatus based on a Hoeken’s Four bar Linkage

Over the last several decades robotic rehabilitation has played an important role in the human-robot interaction. This interaction is usually implemented by means of multi degree of freedom open kinematic chains mechanisms that are very complex and expensive. On the contrary, closed kinematic chains mechanisms based on four- and six bar linkages have only 1-DOF. Nevertheless, such mechanisms are capable of generating paths with complex kinematic characteristics. These mechanisms are preferable when simplicity and cost are the major criteria. These criteria are of higher importance when community based rehabilitation in developing countries is concerned. This capstone project is aimed at synthesizing, designing and manufacturing of such mechanism. The project is based on a 1-DOF mechanism, i.e. Hoeken four bar linkage. Major neurophysiological models related to upper-limb rehabilitation in people after strokes, such as Minimum Jerk Model, Fitts’s Law and Just Noticeable Difference are considered in this paper. The methodology includes developing kinematic, kinetostatic and dynamic analysis of the mechanism along with control and mechatronics concepts. The analysis and concepts derived in this paper are used for patients’ training procedures

Synthesis, Analysis, Design and Manufacturing of an Upper-Limb Rehabilitation Apparatus based on a Hoeken’s Four bar Linkage

Over the last several decades robotic rehabilitation has played an important role in the human-robot interaction. This interaction is usually implemented by means of multi degree of freedom open kinematic chains mechanisms that are very complex and expensive. On the contrary, closed kinematic chains mechanisms based on four- and six bar linkages have only 1-DOF. Nevertheless, such mechanisms are capable of generating paths with complex kinematic characteristics. These mechanisms are preferable when simplicity and cost are the major criteria. These criteria are of higher importance when community based rehabilitation in developing countries is concerned. This capstone project is aimed at synthesizing, designing and manufacturing of such mechanism. The project is based on a 1-DOF mechanism, i.e. Hoeken four bar linkage. Major neurophysiological models related to upper-limb rehabilitation in people after strokes, such as Minimum Jerk Model, Fitts’s Law and Just Noticeable Difference are considered in this paper. The methodology includes developing kinematic, kinetostatic and dynamic analysis of the mechanism along with control and mechatronics concepts. The analysis and concepts derived in this paper are used for patients’ training procedures

Multi-Objective Swarm Intelligence Trajectory Generation for a 7 Degree of Freedom Robotic Manipulator

This work is aimed to demonstrate a multi-objective joint trajectory generation algorithm for a 7 degree of freedom (DoF) robotic manipulator using swarm intelligence (SI)—product of exponentials (PoE) combination. Given a priori knowledge of the end-effector Cartesian trajectory and obstacles in the workspace, the inverse kinematics problem is tackled by SI-PoE subject to multiple constraints. The algorithm is designed to satisfy finite jerk constraint on end-effector, avoid obstacles, and minimize control effort while tracking the Cartesian trajectory. The SI-PoE algorithm is compared with conventional inverse kinematics algorithms and standard particle swarm optimization (PSO). The joint trajectories produced by SI-PoE are experimentally tested on Sawyer 7 DoF robotic arm, and the resulting torque trajectories are compared

Multi-Objective Swarm Intelligence Trajectory Generation for a 7 Degree of Freedom Robotic Manipulator

This work is aimed to demonstrate a multi-objective joint trajectory generation algorithm for a 7 degree of freedom (DoF) robotic manipulator using swarm intelligence (SI)—product of exponentials (PoE) combination. Given a priori knowledge of the end-effector Cartesian trajectory and obstacles in the workspace, the inverse kinematics problem is tackled by SI-PoE subject to multiple constraints. The algorithm is designed to satisfy finite jerk constraint on end-effector, avoid obstacles, and minimize control effort while tracking the Cartesian trajectory. The SI-PoE algorithm is compared with conventional inverse kinematics algorithms and standard particle swarm optimization (PSO). The joint trajectories produced by SI-PoE are experimentally tested on Sawyer 7 DoF robotic arm, and the resulting torque trajectories are compared

A Deep Reinforcement-Learning Approach for Inverse Kinematics Solution of a High Degree of Freedom Robotic Manipulator

The foundation and emphasis of robotic manipulator control is Inverse Kinematics (IK). Due to the complexity of derivation, difficulty of computation, and redundancy, traditional IK solutions pose numerous challenges to the operation of a variety of robotic manipulators. This paper develops a Deep Reinforcement Learning (RL) approach for solving the IK problem of a 7-Degree of Freedom (DOF) robotic manipulator using Product of Exponentials (PoE) as a Forward Kinematics (FK) computation tool and the Deep Q-Network (DQN) as an IK solver. The selected approach is architecturally simpler, making it faster and easier to implement, as well as more stable, because it is less sensitive to hyperparameters than continuous action spaces algorithms. The algorithm is designed to produce joint-space trajectories from a given end-effector trajectory. Different network architectures were explored and the output of the DQN was implemented experimentally on a Sawyer robotic arm. The DQN was able to find different trajectories corresponding to a specified Cartesian path of the end-effector. The network agent was able to learn random Bézier and straight-line end-effector trajectories in a reasonable time frame with good accuracy, demonstrating that even though DQN is mainly used in discrete solution spaces, it could be applied to generate joint space trajectories

Estimation of Uncooperative Satellite Inertia Parameters for Space Debris Removal Using Particle Swarm Optimization

Although passive mitigation measures have been put into place to ensure the long-term sustainability of space activ-ities, numerous studies have shown that in order to stabilize the growth of the orbital debris population, active removal of the largest debris in Earth orbit, such as abandoned spacecraft and rocket bodies, is still necessary. In active debris removal scenarios, the target is generally uncooperative and therefore non-communicative (e.g., through some easily recognizable arti-ficial markers or transponder) with the servicing spacecraft and cannot exchange information and safely perform the docking or berthing operations. Additionally, essential information on the form and inertia characteristics of the space target may have altered due to the prolonged period in orbit (e.g., due to exhaustion of fuel, collisions, or explosions). Additionally, unknown objects such as large debris pieces will have unknown inertia properties. This paper proposes a method of inertia esti-mation of a rotating target assuming a torque-free environment. Estimation is performed through the use of Particle Swarm Optimization (PSO) utilizing attitude observations of the target (quaternion data). The solution space for PSO particles is an R6 vector that can be mapped to inertia tensor matrix space, which represents an estimate of the target's (symmetric) inertia tensor. Attitude motion is propagated using Euler's equations to generate estimated measurements which are then compared to experimental attitude measurements for validatio