In this report, different control techniques for underactuated systems are considered. Underactuated systems are systems that have more degrees of freedom to be controlled than independent control inputs. Several control-techniques are considered for the point-to-point control of underactuated mechanical systems. After that, a control technique is considered for tracking control of underactuate...

We present a method for planning motions of threelink planar robots with a passive rotational third joint in the presence of gravity. These underactuated mechanisms can be fully linearized and input-output decoupled by means of a nonlinear dynamic state feedback, provided that a physical singularity is avoided. The linearizing output is the position of the center of percussion of the third link...

This paper investigates a new modelling and control issue: the tracking control problem of underactuated dynamic systems by using a special example – a pendulum-driven cart-pole system. A dynamic model of a pendulum-driven cart-pole system is firstly presented. Then, a six-step motion strategy of the pendulum-driven cart-pole system is proposed. After that, a desired profile of the pendulum joi...

Analysis of exclusively-kinetic two-link underactuated mechanical systems is undertaken in this paper. It is first shown that such systems are not full-state feedback linearizable around any equilibirium point. Also, the equilibrium points for which the system is small-time locally controllable (STLC) is at most a one dimensional submanifold. A concept less restrictive than STLC, termed the sma...

This contribution presents an approach to achieve trajectory tracking for nonlinear systems. Combining linear regulator theory with the Takagi–Sugeno (T–S) fuzzy methodology; an algorithm is described for this tracking. The main contribution of the paper consists in the real-time application of this algorithm to a specific underactuated robot: the Pendubot.

The authors consider the control of an underactuated mechanical system: Pendubot, which has four separated equilibrium points. A unified controller is proposed to stabilise the system at the four equilibrium points. Moreover, the proposed unified control can bring the underactuated link to ideal homoclinic orbits, which cannot be achieved by existing approaches. Simulation results verify the ef...

This paper combines techniques of potential shaping with those of kinetic shaping to produce some new methods for stabilization of mechanical control systems. As with each of the techniques themselves, our method employs energy methods and the LaSalle invariance principle. We give explicit criteria for asymptotic stabilization of equilibria of mechanical systems which, in the absence of control...

Ball dribbling is a central element of basketball. One main challenge for realizing basketball robots is to stabilize periodic motion of the ball. The task is nontrivial due to the discrete-continuous nature of the corresponding dynamics. This paper proposes to add an elastic element to the manipulator so the ball can be controlled in a continuous-time phase instead of an intermittent contact. ...

A control method without state feedback of the free link is proposed for swing-up and stabilization at the upright position of a flexible free link in a twolink underactuated flexible manipulator (the active first and free second links are rigid and flexible, respectively). The proposed method is based on the actuation of bifurcations produced in the second link under high-frequency excitation ...

Closed-loop, asymptotically stable walking motions are designed for a 5-link, planar bipedal robot model with one degree of underactuation. Parameter optimization is applied to the hybrid zero dynamics, a 1-DOF invariant subdynamics of the full robot model, in order to create asymptotically stable orbits. Tuning the dynamics of this 1 DOF subsystem via optimization is interesting because asympt...