Inverse Kinematics with Dual-Quaternions, Exponential-Maps, and Joint Limits

We present a novel approach for solving articulated inverse kinematic problems (e.g., character structures) by means of an iterative dual-quaternion and exponentialmapping approach. As dual-quaternions are a break from the norm and offer a straightforward and computationally efficient technique for representing kinematic transforms (i.e., position and translation). Dual-quaternions are capable of represent both translation and rotation in a unified state space variable with its own set of algebraic equations for concatenation and manipulation. Hence, an articulated structure can be represented by a set of dual-quaternion transforms, which we can manipulate using inverse kinematics (IK) to accomplish specific goals (e.g., moving end-effectors towards targets). We use the projected Gauss-Seidel iterative method to solve the IK problem with joint limits. Our approach is flexible and robust enough for use in interactive applications, such as games. We use numerical examples to demonstrate our approach, which performed successfully in all our test cases and produced pleasing visual results.Comment: arXiv admin note: substantial text overlap with arXiv:2211.0033

Analysis and synthesis of bipedal humanoid movement : a physical simulation approach

textAdvances in graphics and robotics have increased the importance of tools for synthesizing humanoid movements to control animated characters and physical robots. There is also an increasing need for analyzing human movements for clinical diagnosis and rehabilitation. Existing tools can be expensive, inefficient, or difficult to use. Using simulated physics and motion capture to develop an interactive virtual reality environment, we capture natural human movements in response to controlled stimuli. This research then applies insights into the mathematics underlying physics simulation to adapt the physics solver to support many important tasks involved in analyzing and synthesizing humanoid movement. These tasks include fitting an articulated physical model to motion capture data, modifying the model pose to achieve a desired configuration (inverse kinematics), inferring internal torques consistent with changing pose data (inverse dynamics), and transferring a movement from one model to another model (retargeting). The result is a powerful and intuitive process for analyzing and synthesizing movement in a single unified framework.Computer Science

Real Time Animation of Virtual Humans: A Trade-off Between Naturalness and Control

Virtual humans are employed in many interactive applications using 3D virtual environments, including (serious) games. The motion of such virtual humans should look realistic (or ‘natural’) and allow interaction with the surroundings and other (virtual) humans. Current animation techniques differ in the trade-off they offer between motion naturalness and the control that can be exerted over the motion. We show mechanisms to parametrize, combine (on different body parts) and concatenate motions generated by different animation techniques. We discuss several aspects of motion naturalness and show how it can be evaluated. We conclude by showing the promise of combinations of different animation paradigms to enhance both naturalness and control

PREDICTIVE SIMULATION OF HUMAN MOVEMENT AND APPLICATIONS TO ASSISTIVE DEVICE DESIGN AND CONTROL

Predictive simulation based on dynamic optimization using musculoskeletal models is a powerful approach for studying biomechanics of human gait. Predictive simulation can be used for a variety of applications from designing assistive devices to testing theories of motor controls. However, one of the challenges in formulating the predictive dynamic optimization problem is that the cost function, which represents the underlying goal of the walking task (e.g., minimal energy consumption) is generally unknown and is assumed a priori. While different studies used different cost functions, the qualities of the gaits with those cost functions were often not provided. Therefore, this dissertation evaluates and examines different cost function forms for dynamic simulation of human walking. The problem of the walking cost function determination was cast as a bilevel optimization, which was solved using a nested evolutionary approach. The results showed cost functions based on a weighted combination of muscle-based performance criteria (e.g., metabolic cost, muscle fatigue), gait smoothness, and gait stability led to better walking solutions compared to any cost functions only based on muscle performance criteria. Further evaluations of the walking cost functions were done in the simulation cases of human walking augmented with assistive devices such as prosthesis and exoskeleton. The simulations of augmented walking were comparable to the experimental results, which suggests the potential of using the simulation approach to address problems of finding assistive device design and control

Simulation and Framework for the Humanoid Robot TigerBot

Walking humanoid robotics is a developing field. Different humanoid robots allow for different kinds of testing. TigerBot is a new full-scale humanoid robot with seven degrees-of-freedom legs and with its specifications, it can serve as a platform for humanoid robotics research. Currently TigerBot has encoders set up on each joint, allowing for position control, and its sensors and joints connect to Teensy microcontrollers and the ODroid XU4 single-board computer central control unit. The components’ communication system used the Robot Operating System (ROS). This allows the user to control TigerBot with ROS. It’s important to have a simulation setup so a user can test TigerBot’s capabilities on a model before using the real robot. A working walking gait in the simulation serves as a test of the simulator, proves TigerBot’s capability to walk, and opens further development on other walking gaits. A model of TigerBot was set up using the simulator Gazebo, which allowed testing different walking gaits with TigerBot. The gaits were generated by following the linear inverse pendulum model and the basic zero-moment point (ZMP) concept. The gaits consisted of center of mass trajectories converted to joint angles through inverse kinematics. In simulation while the robot follows the predetermined joint angles, a proportional-integral controller keeps the model upright by modifying the flex joint angle of the ankles. The real robot can also run the gaits while suspended in the air. The model has shown the walking gait based off the ZMP concept to be stable, if slow, and the actual robot has been shown to air walk following the gait. The simulation and the framework on the robot can be used to continue work with this walking gait or they can be expanded on for different methods and applications such as navigation, computer vision, and walking on uneven terrain with disturbances

Predictive Dynamic Simulation of Healthy Sit-to-Stand Movement

This thesis situates itself at the intersection of biomedical modelling and predictive simulation to synthesize healthy human sit-to-stand movement. While the importance of sit-to-stand to physical and social well-being is known, the reasons for why and how people come to perform sit-to-stand the way we do is largely unknown. This thesis establishes the determinants of sit-to-stand in healthy people so that future researchers may investigate the effects of compromised health on sit-to-stand and then explore means of intervening to preserve and restore this motion. Previous researchers have predicted how a person rises from seated. However aspects of their models, most commonly contact and muscle models, are biomechanically inconsistent and restrict their application. These researchers also have not validated their prediction results. To address these limitations and further the study of sit-to-stand prediction, the underlying themes of this thesis are in biomechanical modelling, predictive simulation, and validation. The goal of predicting sit-to-stand inspired the creation of three new models: a model of biomechanics, a model of motion, and performance criteria as a model of preference. First, the human is represented as three rigid links in the sagittal plane. As buttocks are kinetically important to sit-to-stand, a new constitutive model of buttocks is made from experimental force-deformation data. Ten muscles responsible for flexion and extension of the hips, knees, and ankles are defined in the model. Second, candidate sit-to-stand trajectories are described geometrically by a set of Bézier curves, for the first time. Third, with the assumption that healthy people naturally prioritize mechanical efficiency, disinclination to a motion is described as a cost function of joint torques, muscle stresses, and physical infeasibility including slipping and falling. This new dynamic optimization routine allows for motions of gradually increasing complexity, by adding control points to the Bézier curves, while the model's performance is improving. By comparing the predictive simulation results to normative sit-to-stand as described in the literature, for the first time, it is possible to say that the use of these models and optimal control strategy together has produced motions characteristic of healthy sit-to-stand. This work bridges the gap between predictive simulation results and experimental human results and in doing so establishes a benchmark in sit-to-stand prediction. In predicting healthy sit-to-stand, it makes a necessary step toward predicting pathological sit-to-stand, and then to predicting the results of intervention to inform medical design and planning

Predicting the motions and forces of wearable robotic systems using optimal control

Wearable robotic systems are being developed to prevent injury to the low back. Designing a wearable robotic system is challenging because it is difficult to predict how the exoskeleton will affect the movement of the wearer. To aid the design of exoskeletons, we formulate and numerically solve an optimal control problem (OCP) to predict the movements and forces of a person as they lift a 15 kg box from the ground both without (human-only OCP) and with (with-exo OCP) the aid of an exoskeleton. We model the human body as a sagittal-plane multibody system that is actuated by agonist and antagonist pairs of muscle torque generators (MTGs) at each joint. Using the literature as a guide, we have derived a set of MTGs that capture the active torque–angle, passive torque–angle, and torque–velocity characteristics of the flexor and extensor groups surrounding the hip, knee, ankle, lumbar spine, shoulder, elbow, and wrist. Uniquely, these MTGs are continuous to the second derivative and so are compatible with gradient-based optimization. The exoskeleton is modeled as a rigid-body mechanism that is actuated by a motor at the hip and the lumbar spine and is coupled to the wearer through kinematic constraints. We evaluate our results by comparing our predictions with experimental recordings of a human subject. Our results indicate that the predicted peak lumbar-flexion angles and extension torques of the human-only OCP are within the range reported in the literature. The results of the with-exo OCP indicate that the exoskeleton motors should provide relatively little support during the descent to the box but apply a substantial amount of support during the ascent phase. The support provided by the lumbar motor is similar in shape to the net moment generated at the L5/S1 joint by the body; however, the support of the hip motor is more complex because it is coupled to the passive forces that are being generated by the hip extensors of the human subject. The simulations developed in this study are specific to lifting motion and a lower back exoskeleton. However, the framework is applicable for simulating a large range of robotic-assisted human motions