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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.