Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman's controllability. The distance to flatness is measured by a non-negative integer, the defect. We utilize differential algebra where flatness- and defect are best defined without distinguishing between input, state, output and other variables. Many realistic classes of examples are flat. We treat two popular ones: the crane and the car with n trailers, the motion planning of which is obtained via elementary properties of plane curves. The three non-flat examples, the simple, double and variable length pendulums, are borrowed from non-linear physics. A high frequency control strategy is proposed such that the averaged systems become flat.

/pdf/flatness-and-defect-of-non-linear-systems-introductory-42ot9eoqmh.pdf

Flatness and defect of non-linear systems: introductory theory and examples

This paper presents the first randomized approach to kinodynamic planning (also known as trajectory planning or trajectory design). The task is to determine control inputs to drive a robot from an ...

Randomized kinodynamic planning

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems. It is an ideal textbook for undergraduate and graduate students, and is indispensable for researchers seeking a self-contained reference on control theory. Unlike most books on the subject, Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl strm and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. strm and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. They provide exercises at the end of every chapter, and an accompanying electronic solutions manual is available. Feedback Systems is a complete one-volume resource for students and researchers in mathematics, engineering, and the sciences.Covers the mathematics needed to model, analyze, and design feedback systems Serves as an introductory textbook for students and a self-contained resource for researchers Includes exercises at the end of every chapter Features an electronic solutions manual Offers techniques applicable across a range of disciplines

/pdf/feedback-systems-an-introduction-for-scientists-and-596yj6j5hm.pdf

Feedback Systems: An Introduction for Scientists and Engineers

A new system equivalence relation, using the framework of differential geometry of jets and prolongations of infinite order, is studied. In this setting, two systems are said to be equivalent if any variable of one system may be expressed as a function of the variables of the other system and of a finite number of their time derivatives. This is a Lie-Backlund isomorphism. The authors prove that, although the state dimension is not preserved, the number of input channels is kept fixed. They also prove that a Lie-Backlund isomorphism can be realized by an endogenous feedback. The differentially flat nonlinear systems introduced by the authors (1992) via differential algebraic techniques, are generalized and the new notion of orbitally flat systems is defined. They correspond to systems which are equivalent to a trivial one, with time preservation or not. The endogenous linearizing feedback is explicitly computed in the case of the VTOL aircraft to track given reference trajectories with stability.

/pdf/a-lie-backlund-approach-to-equivalence-and-flatness-of-193e40wi0l.pdf

A Lie-Backlund approach to equivalence and flatness of nonlinear systems

A different look at output tracking: control of a VTOL aircraft

A solution of the motion planning without obstacles for the standard a-trailer system is proposed This solution relies basically on the fact that the system is flat with the Cartesian coordinates of the last trailer as a linearizing output The Frenet formulae are used to simplify the calculations and permit to deal with angle constraints The general 1-trailer system, where the trailer is not directly hitched to the car at the center of the rear axle, is also flat The geometric construction used for the standard 1-trailer system can be extended to this more realistic system MATLAB simulations illustrate this method >

/pdf/flatness-motion-planning-and-trailer-systems-2frn4dfys3.pdf

Flatness, motion planning and trailer systems

A revisited quadrotor model is proposed, including in particular the so-called rotor drag. It differs from the model usually considered, even at first order, and much better explains the role of accelerometer feedback in control algorithms. The theoretical derivation is supported by experimental data.

/pdf/the-true-role-of-accelerometer-feedback-in-quadrotor-control-19mpqau85e.pdf

Philippe Martin

Papers

Flatness and defect of non-linear systems: introductory theory and examples

A Lie-Backlund approach to equivalence and flatness of nonlinear systems

A different look at output tracking: control of a VTOL aircraft

Flatness, motion planning and trailer systems

The true role of accelerometer feedback in quadrotor control