PSM: A Predictive Safety Model for Body Motion Based On the Spring-Damper Pendulum

Quantifying the safety of the human body orientation is an important issue in human-robot interaction. Knowing the changing physical constraints on human motion can improve inspection of safe human motions and bring essential information about stability and normality of human body orientations with real-time risk assessment. Also, this information can be used in cooperative robots and monitoring systems to evaluate and interact in the environment more freely. Furthermore, the workspace area can be more deterministic with the known physical characteristics of safety. Based on this motivation, we propose a novel predictive safety model (PSM) that relies on the information of an inertial measurement unit on the human chest. The PSM encompasses a 3-Dofs spring-damper pendulum model that predicts human motion based on a safe motion dataset. The estimated safe orientation of humans is obtained by integrating a safety dataset and an elastic spring-damper model in a way that the proposed approach can realize complex motions at different safety levels. We did experiments in a real-world scenario to verify our novel proposed model. This novel approach can be used in different guidance/assistive robots and health monitoring systems to support and evaluate the human condition, particularly elders.

Discretization and Stabilization of Energy-Based Controller for Period Switching Control and Flexible Scheduling

Emerging advanced control applications, with increased complexity in software but limited computing resources, suggest that real-time controllers should have adaptable designs. These control strategies also should be designed with consideration of the run-time behavior of the system. One of such research attempts is to design the controller along with the task scheduler, known as control-scheduling co-design, for more predictable timing behavior as well as surviving system overloads. Unlike traditional controller designs, which have equal-distance sampling periods, the co-design approach increases the system flexibility and resilience by explicitly considering timing properties, for example using an event-based controller or with multiple sampling times (non-uniform sampling and control). Within this context, we introduce the first work on the discretization of an energy-based controller that can switch arbitrarily between multiple periods and adjust the control parameters accordingly without destabilizing the system. A digital controller design based on this paradigm for a DC motor with an elastic load as an example is introduced and the stability condition is given based on the proposed Lyapunov function. The method is evaluated with various computer-based simulations which demonstrate its effectiveness.

A Novel Assistive Controller Based on Differential Geometry for Users of the Differential-Drive Wheeled Mobile Robots

Certain wheeled mobile robots e.g., electric wheelchairs, can operate through indirect joystick controls from users. Correct steering angle becomes essential when the user should determine the vehicle direction and velocity, in particular for differential wheeled vehicles since the vehicle velocity and direction are controlled with only two actuating wheels. This problem gets more challenging when complex curves should be realized by the user. A novel assistive controller with safety constraints is needed to address these problems. Also, the classic control methods mostly require the desired states beforehand which completely contradicts human's spontaneous decisions on the desired location to go. In this work, we develop a novel assistive control strategy based on differential geometry relying on only joystick inputs and vehicle states where the controller does not require any desired states. We begin with explaining the vehicle kinematics and our designed Darboux frame kinematics on a contact point of a virtual wheel and plane. Next, the geometric controller using the Darboux frame kinematics is designed for having smooth trajectories under certain safety constraints. We experiment our approach with different participants and evaluate its performance in various routes.

Motion Planning of a Spin-Rolling Sphere on a Plane

The paper deals with motion planning for a spin-rolling sphere when the sphere follows a straight path on a plane. Since the motion of the sphere is constrained by the straight line, the control of the sphere's spin motion is essential to converge to a desired configuration of the sphere. In this paper, we show a new geometric-based planning approach that is based on a full-state description of this nonlinear system. First, the problem statement of the motion planning is posed. Next, we develop a geometric controller implemented as a virtual surface by using the Darboux frame kinematics. This virtual surface generates arc-length-based inputs for controlling the trajectories of the sphere. Then, an iterative algorithm is designed to tune these inputs for the desired configurations. The feasibility of the proposed approach is verified by simulations.

Path Planning of a Spin-Rolling Sphere on a Plane

The paper deals with motion planning for a spin-rolling sphere when the sphere follows a straight path on a plane. Since the motion of the sphere is constrained by the straight line, the control of the sphere's spin motion is essential to converge to a desired configuration of the sphere. In this paper, we show a new geometric-based planning approach that is based on a full-state description of this nonlinear system. First, the problem statement of the motion planning is posed. Next, we develop a geometric controller implemented as a virtual surface by using the Darboux frame kinematics. This virtual surface generates arc-length-based inputs for controlling the trajectories of the sphere. Then, an iterative algorithm is designed to tune these inputs for the desired configurations. The feasibility of the proposed approach is verified by simulations.

Darboux-Frame-Based Parametrization for a Spin-Rolling Sphere on a Plane: A Nonlinear Transformation of Underactuated System to Fully-Actuated Model

This paper presents a new kinematic model based on the Darboux-frame for motion control and planning. In this work, we show that an underactuated system as a spin-rolling sphere on a plane with three inputs and five states can be transformed into a fully-actuated model by the given Darboux-frame transformation. This nonlinear state transformation is a geometric model that is different from conventional state-space models. First, a kinematic model of the Darboux frame at the contact point of a rotating object i.e., the sphere, is established. Next, we propose a virtual surface that is trapped between sphere and plane surfaces. This virtual surface generates arc-length-based inputs for controlling the trajectories on the sphere and plane. Finally, we discuss the controllability of this new system after our introduced transformation. In the future, we will design a proper geometric path planning method for the obtained kinematic model.

Line-Circle-Square (LCS): A Multilayered Geometric Filter for Edge-Based Detection

This paper presents a state-of-the-art filter that reduces the complexity in object detection, tracking and mapping applications. Existing edge detection and tracking methods are proposed to create suitable autonomy for mobile robots, however many of them face overconfidence and large computations at the entrance to scenarios with an immense number of landmarks. In particular, it is not practically efficient to solely rely on limited sensors such as a camera. The method in this work, the Line-Circle-Square (LCS) filter, claims that mobile robots without a large database for object recognition and highly advanced prediction methods can deal with incoming objects that the camera captures in real-time. The proposed filter applies detection, tracking and learning to each defined expert to extract more information for judging scenes without over-calculation. The interactive learning feed between each expert creates a minimal error that works against overwhelming detected features in crowded scenes. Our experts are dependent on trust factors' covariance under the geometric definitions to ignore, emerge and compare detected landmarks. The experiment validates the effectiveness of the proposed filter in terms of detection precision and resource usage.

Singularity-Free Inverse Dynamics for Underactuated Systems with a Rotating Mass

Motion control of underactuated systems through the inverse dynamics contains configuration singularities. These limitations in configuration space mainly stem from the inertial coupling that passive joints/bodies create. In this study, we present a model that is free from singularity while the trajectory of the rotating mass has a small-amplitude sine wave around its circle. First, we derive the modified non-linear dynamics for a rolling system. Also, the singularity regions for this underactuated system is demonstrated. Then, the wave parameters are designed under certain conditions to remove the coupling singularities. We obtain these conditions from the positive definiteness of the inertia matrix in the inverse dynamics. Finally, the simulation results are confirmed by using a prescribed Beta function on the specified states of the rolling carrier. Because our algebraic method is integrated into the non-linear dynamics, the proposed solution has a great potential to be extended to the Lagrangian mechanics with multiple degrees-of-freedom.