This paper addresses three control implementation issues for trajectory tracking of robotic manipulators: unmodeled dynamics, unknown input saturation and peaking effects during the transient phase. A model-free first-order robust-adaptive control method is used to deal with the unmodeled dynamics. Robust optimality and stability of the controller are proved using the 𝓗∞ technique and the game-algebraic Riccati equation. An intuitive approach is devised to incorporate the unknown input saturation by modifying the speed of the desired trajectory. The trajectory scaling is performed by using only the state errors. Furthermore, two different techniques are utilized to suppress peaking during the transient response of the trajectory tracking. The first method adds an extra term in the input while the second method uses variable gain to improve the transient response. A systematic procedure for finding the controller parameters is formulated using features, such as rise time and settling time. A three-degree-of-freedom robot manipulator is used for the validation of the proposed controller in simulations and experiments.

Biped robots have gained much attention for decades. A variety of researches have been conducted to make them able to assist or even substitute for humans in performing special tasks. In addition, studying biped robots is important in order to understand human locomotion and to develop and improve control strategies for prosthetic and orthotic limbs. This paper discusses the main challenges encountered in the design of biped robots, such as modeling, stability and their walking patterns. The subject is difficult to deal with because the biped mechanism intervenes with mechanics, control, electronics and artificial intelligence. In this paper, we collect and introduce a systematic discussion of modeling, walking pattern generators and stability for a biped robot.

This paper exploits a natural symmetry present in a 3D robot in order to achieve asymptotically stable steering. The robot under study is composed of 5-links and unactuated point feet; it has 9 DoF (degree-of-freedom) in the single-support phase and six actuators. The control design begins with a hybrid feedback controller that stabilizes a straight-line walking gait for the 3D bipedal robot. The closed-loop system (i.e., robot plus controller) is shown to be equivariant under yaw rotations, and this property is used to construct a modification of the controller that has a local, but uniform, input-to-state stability (ISS) property, where the input is the desired turning direction. The resulting controller is capable of adjusting the net yaw rotation of the robot over a step in order to steer the robot along paths with mild curvature. An interesting feature of this work is that one is able to control the robot's motion along a curved path using only a single predefined periodic motion.

We investigate the possibility of habitable Trojan planets in the HD 23079 star–planet system. This system consists of a solar-type star and a Jupiter-type planet, which orbits the star near the outer edge of the stellar habitable zone in an orbit of low eccentricity. We find that in agreement with previous studies Earth-mass habitable Trojan planets are possible in this system, although the success of staying within the zone of habitability is significantly affected by the orbital parameters of the giant planet and by the initial condition of the theoretical Earth-mass planet. In one of our simulations, the Earth-mass planet is captured by the giant planet and thus becomes a habitable moon.

A stellar evolution computer model has been used to determine changes in the luminosity L and effective temperature Te of single stars during their time on the main sequence. The range of stellar masses investigated was from 0.5 to 1.5 times that of the Sun, each with a mass fraction of metals (metallicity, Z) from 0.008 to 0.05. The extent of each star's habitable zone (HZ) has been determined from its values of L and Te. These stars form a reference framework for other main sequence stars. All of the 104 main sequence stars known to have one or more giant planets have been matched to their nearest stellar counterpart in the framework, in terms of mass and metallicity, hence closely approximating their HZ limits. The limits of HZ, for each of these stars, have been compared to their giant planet(s)'s range of strong gravitational influence. This allows a quick assessment as to whether Earth-mass planets could exist in stable orbits within the HZ of such systems, both presently and at any time during the star's main sequence lifetime. A determination can also be made as to the possible existence of life-bearing satellites of giant planets, which orbit within HZs. Results show that about half of the 104 known extrasolar planetary systems could possibly have been housing an Earth-mass planet in HZs during at least the past billion years, and about three-quarters of the 104 could do so for at least a billion years at some time during their main sequence lives. Whether such Earth-mass planets could have formed is an urgent question now being investigated by others, with encouraging results.