H. Harry Asada

Jerry Ng, H. Harry Asada

This paper presents a Koopman lifting linearization method that is applicable to nonlinear dynamical systems having both stable and unstable regions. It is known that DMD and other standard data-driven methods face a fundamental difficulty in constructing a Koopman model when applied to unstable systems. Here we solve the problem by incorporating knowledge about a nonlinear state equation with a learning method for finding an effective set of observables. In a lifted space, stable and unstable regions are separated into independent subspaces. Based on this property, we propose to find effective observables through neural net training where training data are separated into stable and unstable trajectories. The resultant learned observables are used for constructing a linear state transition matrix using method known as Direct Encoding, which transforms the nonlinear state equation to a state transition matrix through inner product computations with the observables. The proposed method shows a dramatic improvement over existing DMD and data-driven methods.

John Bell, H. Harry Asada

In providing physical assistance to elderly people, ensuring cooperative behavior from the elderly persons is a critical requirement. In sit-to-stand assistance, for example, an older adult must lean forward, so that the body mass can shift towards the feet before a caregiver starts lifting the body. An experienced caregiver guides the older adult through verbal communications and physical interactions, so that the older adult may be cooperative throughout the process. This guidance is of paramount importance and is a major challenge in introducing a robotic aid to the eldercare environment. The wide-scope goal of the current work is to develop an intelligent eldercare robot that can a) monitor the mental state of an older adult, and b) guide the older adult through an assisting procedure so that he/she can be cooperative in being assisted. The current work presents a basic modeling framework for describing a human's physical behaviors reflecting an internal mental state, and an algorithm for estimating the mental state through interactive observations. The sit-to-stand assistance problem is considered for the initial study. A simple Kalman Filter is constructed for estimating the level of cooperativeness in response to applied cues, with a thresholding scheme being used to make judgments on the cooperativeness state.

Jianwen Luo, Sicong Liu, Chengyu Lin et al.

Supernumerary Robotics Device (SRD) is an ideal solution to provide robotic assistance in overhead manual manipulation. Since two arms are occupied for the overhead task, it is desired to have additional arms to assist us in achieving other subtasks such as supporting the far end of a long plate and pushing it upward to fit in the ceiling. In this study, a method that maps human muscle force to SRD for overhead task assistance is proposed. Our methodology is to utilize redundant DoFs such as the idle muscles in the leg to control the supporting force of the SRD. A sEMG device is worn on the operator's shank where muscle signals are measured, parsed, and transmitted to SRD for control. In the control aspect, we adopted stiffness control in the task space based on torque control at the joint level. We are motivated by the fact that humans can achieve daily manipulation merely through simple inherent compliance property in joint driven by muscles. We explore to estimate the force of some particular muscles in humans and control the SRD to imitate the behaviors of muscle and output supporting forces to accomplish the subtasks such as overhead supporting. The sEMG signals detected from human muscles are extracted, filtered, rectified, and parsed to estimate the muscle force. We use this force information as the intent of the operator for proper overhead supporting force. As one of the well-known compliance control methods, stiffness control is easy to achieve using a few of straightforward parameters such as stiffness and equilibrium point. Through tuning the stiffness and equilibrium point, the supporting force of SRD in task space can be easily controlled. The muscle force estimated by sEMG is mapped to the desired force in the task space of the SRD. The desired force is transferred into stiffness or equilibrium point to output the corresponding supporting force.

Filippos E. Sotiropoulos, H. Harry Asada

A lifting-linearization method based on the Koopman operator and Dual Faceted Linearization is applied to the control of a robotic excavator. In excavation, a bucket interacts with the surrounding soil in a highly nonlinear and complex manner. Here, we propose to represent the nonlinear bucket-soil dynamics with a set of linear state equations in a higher-dimensional space. The space of independent state variables is augmented by adding variables associated with nonlinear elements involved in the bucket-soil dynamics. These include nonlinear resistive forces and moment acting on the bucket from the soil, and the effective inertia of the bucket that varies as the soil is captured into the bucket. Variables associated with these nonlinear resistive and inertia elements are treated as additional state variables, and their time evolution is represented as another set of linear differential equations. The lifted linear dynamic model is then applied to Model Predictive Contouring Control, where a cost functional is minimized as a convex optimization problem thanks to the linear dynamics in the lifted space. The lifted linear model is tuned based on a data-driven method by using a soil dynamics simulator. Simulation experiments verify the effectiveness of the proposed lifting linearization compared to its counterpart.

Nicholas Stearns Selby, H. Harry Asada

Effective and causal observable functions for low-order lifting linearization of nonlinear controlled systems are learned from data by using neural networks. While Koopman operator theory allows us to represent a nonlinear system as a linear system in an infinite-dimensional space of observables, exact linearization is guaranteed only for autonomous systems with no input, and finding effective observable functions for approximation with a low-order linear system remains an open question. Dual-Faceted Linearization uses a set of effective observables for low-order lifting linearization, but the method requires knowledge of the physical structure of the nonlinear system. Here, a data-driven method is presented for generating a set of nonlinear observable functions that can accurately approximate a nonlinear control system to a low-order linear control system. A caveat in using data of measured variables as observables is that the measured variables may contain input to the system, which incurs a causality contradiction when lifting the system, i.e. taking derivatives of the observables. The current work presents a method for eliminating such anti-causal components of the observables and lifting the system using only causal observables. The method is applied to excavation automation, a complex nonlinear dynamical system, to obtain a low-order lifted linear model for control design.

Daniel J. Gonzalez, H. Harry Asada

The Extra Robotic Legs (XRL) system is a robotic augmentation worn by a human operator consisting of two articulated robot legs that walk with the operator and help bear a heavy backpack payload. It is desirable for the Human-XRL quadruped system to walk with the rear legs lead the front by 25% of the gait period, minimizing the energy lost from foot impacts while maximizing balance stability. Unlike quadrupedal robots, the XRL cannot command the human's limbs to coordinate quadrupedal locomotion. Using a pair of Rimless Wheel models, it is shown that the systems coupled with a spring and damper converge to the desired 25% phase difference. A Poincaré return map was generated using numerical simulation to examine the convergence properties to different coupler design parameters, and initial conditions. The Dynamically Coupled Double Rimless Wheel system was physically realized with a spring and dashpot chosen from the theoretical results, and initial experiments indicate that the desired synchronization properties may be achieved within several steps using this set of passive components alone.

Daniel J. Gonzalez, H. Harry Asada

A new approach to the human-robot shared control of the Extra Robotic Legs (XRL) wearable augmentation system is presented. The XRL system consists of two extra legs that bear the entirety of its backpack payload, as well as some of the human operator's weight. The XRL System must support its own balance and assist the operator stably while allowing them to move in selected directions. In some directions of the task space the XRL must constrain the human motion with position feedback for balance, while in other directions the XRL must have no position feedback, so that the human can move freely. Here, we present Hybrid Open-Loop / Closed-Loop Control Architecture for mixing the two control modes in a systematic manner. The system is reduced to individual joint feedback control that is simple to implement and reliable against failure. The method is applied to the XRL system that assists a human in conducting a nuclear waste decommissioning task. A prototype XRL system has been developed and demonstrated with a simulated human performing the transition from standing to crawling and back again while coupled to the prototype XRL system.

Daniel J. Gonzalez, H. Harry Asada

We present the design of a new robotic human augmentation system that will assist the operator in carrying a heavy payload, reaching and maintaining difficult postures, and ultimately better performing their job. The Extra Robotic Legs (XRL) system is worn by the operator and consists of two articulated robotic legs that move with the operator to bear a heavy payload. The design was driven by a need to increase the effectiveness of hazardous material emergency response personnel who are encumbered by their personal protective equipment (PPE). The legs will ultimately walk, climb stairs, crouch down, and crawl with the operator while eliminating all external PPE loads on the operator. The forces involved in the most extreme loading cases were analyzed to find an effective strategy for reducing actuator loads. The analysis reveals that the maximum torque is exerted during the transition from the crawling to standing mode of motion. Peak torques are significantly reduced by leveraging redundancy in force application resulting from a closed-loop kinematic chain formed by a particular posture of the XRL. The actuators, power systems, and transmission elements were designed from the results of these analyses. Using differential mechanisms to combine the inputs of multiple actuators into a single degree of freedom, the gear reductions needed to bear the heavy loads could be kept at a minimum, enabling high bandwidth force control due to the near-direct-drive transmission. A prototype was fabricated utilizing the insights gained from these analyses and initial tests indicate the feasibility of the XRL system.

Daniel J. Gonzalez, H. Harry Asada

A new type of parallel robot mechanism with an extendable structure is presented, and its kinematic properties and design parameters are analyzed. The Triple Scissor Extender (TSE) is a 6 Degree-Of-Freedom robotic mechanism for reaching high ceilings and positioning an end effector. Three scissor mechanisms are arranged in parallel, with the bottom ends coupled to linear slides, and the top vertex attached to an end effector plate. Arbitrary positions and orientations of the end effector can be achieved through the coordinated motion of the six linear actuators located at the base. By changing key geometric parameters, the TSE's design can yield a specific desired workspace volume and differential motion behavior. A general kinematic model for diverse TSEs is derived, and the kinematic properties, including workspace, singularity, and the Jacobian singular values, are evaluated. From these expressions, four key design parameters are identified, and their sensitivity upon the workspace volume and the Jacobian singular values is analyzed. A case study in autonomous aircraft assembly is presented using the insights gained from the design parameter studies.

Daniel J. Gonzalez, H. Harry Asada

We present a novel 6 DOF robotic mechanism for reaching high ceilings and positioning an end-effector. The end-effector is supported with three scissor mechanisms that extend towards the ceiling with 6 independent linear actuators moving the base ends of the individual scissors. The top point of each scissor is connected to one of three ball joints located at the three vertices of the top triangular plate holding the end-effector. Coordinated motion of the 6 linear actuators at the base allows the end-effector to reach an arbitrary position with an arbitrary orientation. The design concept of the Triple Scissor Extender is presented, followed by kinematic modeling and analysis of the the Inverse Jacobian relating actuator velocities to the end-effector velocities. The Inverse Jacobian eigenvalues are determined for diverse configurations in order to characterize the kinematic properties. A proof-of-concept prototype has been designed and built. The Inverse Jacobian for use in differential control is evaluated through experiments.