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The optimization of motion and trajectory planning is an effective and usually costless approach to improving the performance of robots, mechatronic systems, automatic machines and multibody systems. Indeed, wise planning increases precision and machine productivity, while reducing vibrations, motion time, actuation effort and energy consumption. On the other hand, the availability of optimized methods for motion planning allows for a cheaper and lighter system construction. The issue of motion planning is also tightly linked with the synthesis of high-performance feedback and feedforward control schemes, which can either enhance the effectiveness of motion planning or compensate for its gaps. To collect and disseminate a meaningful collection of these applications, this book proposes 15 novel research studies that cover different sub-areas, in the framework of motion planning and control.

History of engineering & technology --- humanoid robot --- walk fast --- rotational slip --- ZMP --- gait planning --- quadruped robot --- whole robot control --- location trajectory --- dynamic gait --- fin stabilizer --- command-filtered backstepping --- sliding mode control --- prescribed performance --- disturbance observer --- OES --- inertial stability accuracy --- low-speed performance --- speed observation --- disturbance observation --- state-augmented Kalman filter --- composed control scheme --- fractional calculus --- FOPD controller --- underwater vehicle --- motion control --- modal analysis --- flexible multibody systems --- linearized models --- six-legged robot --- whole-body motion planning --- rugged terrain --- support --- swing --- gesture-based teleoperation --- robotic assembly --- force feedback --- compliant robot motion --- pickup manipulator --- adaptive genetic algorithm --- trajectory optimization --- improved artificial potential field method --- obstacle avoidance planning --- robust estimation --- dynamic model --- unknown but bounded noise --- extended set-membership filter --- dynamic balancing --- shaking force balancing --- acceleration control of the center of mass --- fully Cartesian coordinates --- natural coordinates --- parallel manipulators --- passive model --- biped walking --- Impact and contact --- friction force --- dissipative force --- energy efficiency --- robot --- motion design --- functional redundancy --- UR5 --- hybrid navigation system --- weighted-sum model --- a heuristic algorithm --- piecewise cubic Bézier curve --- mobile robot --- humanoid robot --- walk fast --- rotational slip --- ZMP --- gait planning --- quadruped robot --- whole robot control --- location trajectory --- dynamic gait --- fin stabilizer --- command-filtered backstepping --- sliding mode control --- prescribed performance --- disturbance observer --- OES --- inertial stability accuracy --- low-speed performance --- speed observation --- disturbance observation --- state-augmented Kalman filter --- composed control scheme --- fractional calculus --- FOPD controller --- underwater vehicle --- motion control --- modal analysis --- flexible multibody systems --- linearized models --- six-legged robot --- whole-body motion planning --- rugged terrain --- support --- swing --- gesture-based teleoperation --- robotic assembly --- force feedback --- compliant robot motion --- pickup manipulator --- adaptive genetic algorithm --- trajectory optimization --- improved artificial potential field method --- obstacle avoidance planning --- robust estimation --- dynamic model --- unknown but bounded noise --- extended set-membership filter --- dynamic balancing --- shaking force balancing --- acceleration control of the center of mass --- fully Cartesian coordinates --- natural coordinates --- parallel manipulators --- passive model --- biped walking --- Impact and contact --- friction force --- dissipative force --- energy efficiency --- robot --- motion design --- functional redundancy --- UR5 --- hybrid navigation system --- weighted-sum model --- a heuristic algorithm --- piecewise cubic Bézier curve --- mobile robot

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Splines, both interpolatory and smoothing, have a long and rich history that has largely been application driven. This book unifies these constructions in a comprehensive and accessible way, drawing from the latest methods and applications to show how they arise naturally in the theory of linear control systems. Magnus Egerstedt and Clyde Martin are leading innovators in the use of control theoretic splines to bring together many diverse applications within a common framework. In this book, they begin with a series of problems ranging from path planning to statistics to approximation. Using the tools of optimization over vector spaces, Egerstedt and Martin demonstrate how all of these problems are part of the same general mathematical framework, and how they are all, to a certain degree, a consequence of the optimization problem of finding the shortest distance from a point to an affine subspace in a Hilbert space. They cover periodic splines, monotone splines, and splines with inequality constraints, and explain how any finite number of linear constraints can be added. This book reveals how the many natural connections between control theory, numerical analysis, and statistics can be used to generate powerful mathematical and analytical tools. This book is an excellent resource for students and professionals in control theory, robotics, engineering, computer graphics, econometrics, and any area that requires the construction of curves based on sets of raw data.

Interpolation. --- Smoothing (Numerical analysis) --- Smoothing (Statistics) --- Curve fitting. --- Splines. --- Spline theory. --- Spline functions --- Approximation theory --- Interpolation --- Joints (Engineering) --- Mechanical movements --- Harmonic drives --- Fitting, Curve --- Numerical analysis --- Least squares --- Statistics --- Curve fitting --- Graduation (Statistics) --- Roundoff errors --- Graphic methods --- Accuracy and precision. --- Affine space. --- Affine variety. --- Algorithm. --- Approximation. --- Arbitrarily large. --- B-spline. --- Banach space. --- Bernstein polynomial. --- Bifurcation theory. --- Big O notation. --- Birkhoff interpolation. --- Boundary value problem. --- Bézier curve. --- Chaos theory. --- Computation. --- Computational problem. --- Condition number. --- Constrained optimization. --- Continuous function (set theory). --- Continuous function. --- Control function (econometrics). --- Control theory. --- Controllability. --- Convex optimization. --- Convolution. --- Cubic Hermite spline. --- Data set. --- Derivative. --- Differentiable function. --- Differential equation. --- Dimension (vector space). --- Directional derivative. --- Discrete mathematics. --- Dynamic programming. --- Equation. --- Estimation. --- Filtering problem (stochastic processes). --- Gaussian quadrature. --- Gradient descent. --- Gramian matrix. --- Growth curve (statistics). --- Hermite interpolation. --- Hermite polynomials. --- Hilbert projection theorem. --- Hilbert space. --- Initial condition. --- Initial value problem. --- Integral equation. --- Iterative method. --- Karush–Kuhn–Tucker conditions. --- Kernel method. --- Lagrange polynomial. --- Law of large numbers. --- Least squares. --- Linear algebra. --- Linear combination. --- Linear filter. --- Linear map. --- Mathematical optimization. --- Mathematics. --- Maxima and minima. --- Monotonic function. --- Nonlinear programming. --- Nonlinear system. --- Normal distribution. --- Numerical analysis. --- Numerical stability. --- Optimal control. --- Optimization problem. --- Ordinary differential equation. --- Orthogonal polynomials. --- Parameter. --- Piecewise. --- Pointwise. --- Polynomial interpolation. --- Polynomial. --- Probability distribution. --- Quadratic programming. --- Random variable. --- Rate of convergence. --- Ratio test. --- Riccati equation. --- Simpson's rule. --- Simultaneous equations. --- Smoothing spline. --- Smoothing. --- Smoothness. --- Special case. --- Spline (mathematics). --- Spline interpolation. --- Statistic. --- Stochastic calculus. --- Stochastic. --- Telemetry. --- Theorem. --- Trapezoidal rule. --- Waypoint. --- Weight function. --- Without loss of generality.

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The optimization of motion and trajectory planning is an effective and usually costless approach to improving the performance of robots, mechatronic systems, automatic machines and multibody systems. Indeed, wise planning increases precision and machine productivity, while reducing vibrations, motion time, actuation effort and energy consumption. On the other hand, the availability of optimized methods for motion planning allows for a cheaper and lighter system construction. The issue of motion planning is also tightly linked with the synthesis of high-performance feedback and feedforward control schemes, which can either enhance the effectiveness of motion planning or compensate for its gaps. To collect and disseminate a meaningful collection of these applications, this book proposes 15 novel research studies that cover different sub-areas, in the framework of motion planning and control.

History of engineering & technology --- humanoid robot --- walk fast --- rotational slip --- ZMP --- gait planning --- quadruped robot --- whole robot control --- location trajectory --- dynamic gait --- fin stabilizer --- command-filtered backstepping --- sliding mode control --- prescribed performance --- disturbance observer --- OES --- inertial stability accuracy --- low-speed performance --- speed observation --- disturbance observation --- state-augmented Kalman filter --- composed control scheme --- fractional calculus --- FOPD controller --- underwater vehicle --- motion control --- modal analysis --- flexible multibody systems --- linearized models --- six-legged robot --- whole-body motion planning --- rugged terrain --- support --- swing --- gesture-based teleoperation --- robotic assembly --- force feedback --- compliant robot motion --- pickup manipulator --- adaptive genetic algorithm --- trajectory optimization --- improved artificial potential field method --- obstacle avoidance planning --- robust estimation --- dynamic model --- unknown but bounded noise --- extended set-membership filter --- dynamic balancing --- shaking force balancing --- acceleration control of the center of mass --- fully Cartesian coordinates --- natural coordinates --- parallel manipulators --- passive model --- biped walking --- Impact and contact --- friction force --- dissipative force --- energy efficiency --- robot --- motion design --- functional redundancy --- UR5 --- hybrid navigation system --- weighted-sum model --- a heuristic algorithm --- piecewise cubic Bézier curve --- mobile robot --- n/a

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The optimization of motion and trajectory planning is an effective and usually costless approach to improving the performance of robots, mechatronic systems, automatic machines and multibody systems. Indeed, wise planning increases precision and machine productivity, while reducing vibrations, motion time, actuation effort and energy consumption. On the other hand, the availability of optimized methods for motion planning allows for a cheaper and lighter system construction. The issue of motion planning is also tightly linked with the synthesis of high-performance feedback and feedforward control schemes, which can either enhance the effectiveness of motion planning or compensate for its gaps. To collect and disseminate a meaningful collection of these applications, this book proposes 15 novel research studies that cover different sub-areas, in the framework of motion planning and control.

humanoid robot --- walk fast --- rotational slip --- ZMP --- gait planning --- quadruped robot --- whole robot control --- location trajectory --- dynamic gait --- fin stabilizer --- command-filtered backstepping --- sliding mode control --- prescribed performance --- disturbance observer --- OES --- inertial stability accuracy --- low-speed performance --- speed observation --- disturbance observation --- state-augmented Kalman filter --- composed control scheme --- fractional calculus --- FOPD controller --- underwater vehicle --- motion control --- modal analysis --- flexible multibody systems --- linearized models --- six-legged robot --- whole-body motion planning --- rugged terrain --- support --- swing --- gesture-based teleoperation --- robotic assembly --- force feedback --- compliant robot motion --- pickup manipulator --- adaptive genetic algorithm --- trajectory optimization --- improved artificial potential field method --- obstacle avoidance planning --- robust estimation --- dynamic model --- unknown but bounded noise --- extended set-membership filter --- dynamic balancing --- shaking force balancing --- acceleration control of the center of mass --- fully Cartesian coordinates --- natural coordinates --- parallel manipulators --- passive model --- biped walking --- Impact and contact --- friction force --- dissipative force --- energy efficiency --- robot --- motion design --- functional redundancy --- UR5 --- hybrid navigation system --- weighted-sum model --- a heuristic algorithm --- piecewise cubic Bézier curve --- mobile robot --- n/a