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Abstract The field of tensegrity faces challenges in design to facilitate efficient fabrication, and modeling due to the antagonistic nature of tension and compression elements. The research presents design methodology, and modeling framework for a human-spine inspired Dexterous continuum Tensegrity manipulatoR (DexTeR). DexTeR is a continuum manipulator that comprises of an assembly of “vertebra” modules fabricated using two curved links and 12 strings, and actuated using motor-tendon actuators. The fabrication methodology involves the construction of the equivalent graph of the module and finding the Euler path that traverses every edge of the graph exactly once. The vertices and edges of the graph correspond to the holes and strings or links of the mechanism. Unlike traditional rigid manipulators, the design results in centralization of the majority of the weight of the actuators at the base with negligible effect on the manipulator dynamics. For the first time in literature, we fabricate a tensegrity manipulator that is assembled using ten modules to conceptually validate the time and cost efficiency of the approach. A dynamic model of a vertebra module is presented using the Euler–Newton approach with screw theory representation. Each rigid link is represented using a screw, a six-dimensional vector with components of angular rotation, and linear translation. The nonlinearity in the system arises from the discontinuous behavior of the strings and the “closed-chain” nature of the mechanism. The behavior of the strings is piece-wise continuous to model their slack, compliant, or tension states. 

The balance of inverted pendulum on inclined surfaces is the precursor to their control in unstructured environments. Researchers have devised control algorithms with feedback from contact (encoders - placed at the pendulum joint) and non-contact (gyroscopes, tilt) sensors. We present feedback control of Inverted Pendulum Cart (IPC) on variable inclines using non-contact sensors and a modified error function. The system is in the state of equilibrium when it is not accelerating and not falling over (rotational equilibrium). This is achieved when the pendulum is aligned along the gravity vector. The control feedback is obtained from non-contact sensors comprising of a pair of accelerometers placed on the inverted pendulum and one on the cart. The proposed modified error function is composed of the dynamic (non-gravity) acceleration of the pendulum and the velocity of the cart. We prove that the system is in equilibrium when the modified error is zero. We present algorithm to calculate the dynamic acceleration and angle of the pendulum, and incline angle using accelerometer readings. Here, the cart velocity and acceleration are assumed to be proportional to the motor angular velocity and acceleration. Thereafter, we perform simulation using noisy sensors to illustrate the balance of IPC on surfaces with unknown inclination angles using PID feedback controller with saturated motor torque, including valley profile that resembles a downhill, flat and uphill combination. The successful control of the system using the proposed modified error function and accelerometer feedback argues for future design of controllers for unstructured and unknown environments using all-accelerometer feedback. 

Over the last few decades, Gyro-Free Inertial Measurement Units (GF-IMUs) have been extensively researched to overcome the limitations of gyroscopes. This research presents a Non-coplanar Accelerometer Array (NAA) for estimating angular velocity with non-specific geometric arrangement of four or more triaxial accelerometers with non-coplanarity constraint. The presented proof of non-coplanar spacial arrangement also provides insights into propagation of the sensor noise and construction of the noise covariance matrices. The system noise depends on the singular values of the relative displacement matrix (between the sensors). A dynamical system model with uncorrelated process and measurement noise is proposed where the accelerometer readings are used simultaneously as process and measurement inputs. The angular velocity is estimated using an Extended Kalman Filter (EKF) that discretizes and linearizes the continuous-discrete time dynamical system. The simulations are performed on a Cube-NAA (Cu-NAA) comprising four accelerometers placed at different vertices of a cube.They analyze the estimation error for static and dynamic movement as the distance between the accelerometers (four accelerometers in cube-orientation) is varied. Here, the system noise is observed to decrease inversely with the length of the cube edge as the arrangement is kept identical. Consequently, the simulation results indicate asymptotic decrease in the standard error of estimation with edge length. The experiments are conducted on a Cu-NAA with five reflective optical markers. The reflective markers are visually tracked using Vicon® to construct the ground truth angular velocity. This unique experimental setup, apart from providing three degrees of rotational freedom of movement, also allows for three degrees of spacial translation (linear acceleration of the Cu-NAA in space). The simulation and experimental results indicate better performance of the proposed EKF as compared to one with correlated process and measurement noises. 

Patients suffering from medical conditions resulting in hand impairment experience difficulty in performing simple daily tasks, like getting dressed or using a pencil, resulting in a poorer quality of life. Rehabilitation attempts to help such individuals regain a sense of control and normalcy. In this context, recent advances in robotics have manifested in multiple designs of hand exoskeletons and exosuit gloves for assistance and rehabilitation. These designs are typically actuated using pneumatic, shape memory alloys and motor-tendon actuators. The proposed Motor Tendon Actuated Exosuit Glove (MTAEG) with an open palm is a soft material glove capable of both flexion and extension of all four fingers of the human hand. Its minimally invasive design maintains an open palm to facilitate haptic and tactile interaction with the environment. The MTAEG achieves flexion-extension motion with joint angles of 45° at the metacarpal joint which is 57% of the desired motion; 90° at the proximal interphalangeal joint which is 100% of the desired motion; and 50° at the distal interphalangeal joint which is 96% of the desired motion. The paper discusses the challenges in achieving the desired motion without the ability to directly model human tendons, and the inability to actuate joints individually.