# Optimization of Motion Planning and Control for Automatic Machines, Robots and Multibody Systems
## 2 Book Overview
### Motion Planning  
The issue of energy reduction in robotic systems through motion planning is discussed in [9], where the functional redundancy of a robotic system is exploited to enhance energy efficiency. Indeed, whenever the number of degrees of freedom required to complete the task is smaller than the number of available degrees of freedom of the system, such a redundancy can be exploited by choosing, among the sequence of infinite solutions of the inverse kinematic problem, those ensuring minimum energy consumption. This result proves that motion planning is a costless approach to reduce the energy impact of robotic systems.  
In [10], trajectory optimization is aimed at improving obstacle avoidance in industrial robots. The method proposed therein is based on the improved artificial potential field method and the cosine adaptive genetic algorithm. The artificial potential field method is used to establish the attraction, repulsion, and resultant potential field functions. According to the motion constraint conditions, the fitness function is designed, and the relation between fitness function and motion constraint is analyzed. The results show that the manipulator can avoid obstacles and smoothly reach the target point along the path of obstacle avoidance planning. When the obstacle point is close to the target point, the improved artificial potential field method can avoid the end-effector swing between the obstacle point and the target point and solve the problem of the unreachable target.  
One relevant problem in the operation of many industrial robots is the transmission of vibrations to the fixed frame during their high-speed motion, due to unbalanced inertia forces. A very important research topic is finding new methods to remove or decrease these alternating dynamic loads transmitted to the base and, therefore, to allow for the increase in the operating velocities. This issue is discussed in [11] through a \"3 RRR\" planar parallel manipulator, by proposing a mixed technique, combining balancing by redistributing the mass and the kinematic guidance of the end-effector using a proper motion profile.  
The application of obstacle avoidance is also investigated for the case of mobile robots in [12], to meet the ever-growing use of such systems. This paper proposes some real-time algorithms for the navigation of an autonomous service robot in an indoor environment in the presence of moving obstacles. The reshape trajectory method is exploited. Experimental results through a two-wheel differential drive mobile robot show the method's effectiveness.  
Among mobile robots, legged robots are attracting interest in the scientific community, and therefore have been included in this book. In [13], the whole-body motion planning of a six-legged robot over rugged terrain is discussed. Motion planning is decomposed into support motion (aimed at stability maximization and orientation matching) and swing motion. The latter problem is solved as an optimization problem, which minimizes a bioinspired objective function. Both simulations and experiments validate the proposed whole-body motion planning method.  
A two-legged humanoid robot is instead investigated in [14]. Starting from a spatial three-mass model, where both the trunk and thighs are regarded as an inverted pendulum, while the shanks and feet are considered as mass-points under no constraints with the trunk, a friction constraint method is proposed to plan the trajectory of the leg swing. The goal of optimal motion planning has been assumed to be achieving the fastest walking speed without any rotational slip. The numerical results show that, by using the friction constraint method proposed, the maximum walking speed without rotational slip can be obtained.