Soft and hyper-elastic materials possess properties of resilience and flexibility, characterizing a class of Soft-Continuum Manipulators (SCM). The latter describes a robot structure with an infinite number of degrees of freedom (DoFs), useful for mobility and manipulation. However, these geometric characteristics are source of modeling and control problems. In this paper, a Pythagorean Hodograph (PH) curve based Reduced-Order-Model (ROM) relying on the Gauss-Lobatto quadrature is investigated for the modeling and the control of SCM. This allows, first, reducing the dimension of the SCM kinematics based on the PH parametric curves with a predefined length and second, developing the shape kinematics control from its control polygon. The use of the Gauss-Lobatto quadrature allows to move independently the PH curve control points, while preserving PH features of length and minimum curve energy. These features are important to control in real-time the shape of the SCM. The proposed approach has been validated numerically and experimentally, carried out on a bio-inspired Soft continuum Elephant Trunk Robot.

We present an analysis of a point mass, point foot, planar inverted pendulum model for bipedal walking. Using this model, we derive expressions for a conserved quantity, the "orbital energy", given a smooth center of mass trajectory. Given a closed form center of mass trajectory, the equation for the orbital energy is a closed form expression except for an integral term, which we show to be the first moment of area under the center of mass path. Hence, given a center of mass trajectory, it is straightforward and computationally simple to compute phase portraits for the system. In fact, for many classes of trajectories, such as those in which height is a polynomial function of center of mass horizontal displacement, the orbital energy can be solved in closed form. Given expressions for the orbital energy, we can compute where the foot should be placed or how the center of mass trajectory should be modified in order to achieve a desired velocity on the next step. We demonstrate our results using a planar biped simulation with light legs and point mass body. We parameterize the center of mass trajectory with a fifth order polynomial function. We demonstrate how the parameters of this polynomial and step length can be changed in order to achieve a desired next step velocity.

The approach presented is this paper is based on two ideas: (1) on the planning level an electrostatic potential field in the configuration space of the robot is used. The generalized force curves are attractive to the goal point avoiding obstacles without local minima; (2) on the control level the system follows these force curves using sliding mode control. The system is attracted to the swiching manifold using sliding mode and therewith the systkm is robust to disturbances and parameter variations. the system control variables so that sliding mode occurs in the vicinity of the force field curves and the system is attracted to them. This means that the system trajectories are identical to the force field curves. Sliding mode assures robust control performance despite unknown disturbances and parameter variations.

The approach described consists in constructing potential fields in configuration space like an electrostatic one with changes distributed in such a way that the generalized force curves are attracted to the goal point and avoid obstacles. The system follows such force curves by using sliding mode. The strategy of robot path obstacle avoidance control with sliding mode is presented and discussed in the two-dimensional space.>