Inverse dynamics
Encyclopedia
Inverse dynamics is an inverse problem
. It commonly refers to either inverse rigid body dynamics or inverse structural dynamics
. Inverse rigid-body dynamics is a method for computing forces and/or moments of force (torques) based on the kinematics
(motion) of a body and the body's inertial properties (mass
and moment of inertia
). Typically it uses link-segment models to represent the mechanical behaviour of interconnected segments, such as the limb
s of humans, animals or robot
s, where given the kinematics of the various parts, inverse dynamics derives the minimum forces and moments responsible for the individual movements. In practice, inverse dynamics computes these internal moments and forces from measurements of the motion of limbs and external forces such as ground reaction force
s, under a special set of assumptions.
and biomechanics
constitute the major application areas for inverse dynamics.
Within robotics
, inverse dynamics algorithms are used to calculate the torque
s that a robot's motors must deliver to make the robot's end-point move in the way prescribed by its current task. The "inverse dynamics problem" in Robotics Engineering was solved by Eduardo Bayo
in 1987. This solution calculates how each of the numerous electric motors that control a robot arm must move to produce a particular action. Humans can perform very complicated and precise movements, such as controlling the tip of a fishing rod well enough to cast the bait accurately. Before the arm moves, the brain calculates the necessary movement of each muscle involved and tells the muscles what to do as the arm swings. In the case of a robot arm, the "muscles" are the electric motors which must turn by a given amount at a given moment. Each motor must be supplied with just the right amount of electrical current, at just the right time. Researchers can predict the motion of a robot arm if they know how the motors will move. This is known as the forward dynamics problem. Until this discovery, they had not been able to work backwards to calculate the movements of the motors required to generate a particular complicated motion., Bayo's work began with the application of frequency-domain methods to the inverse dynamics of single-link flexible robots. This approach yielded non-causal exact solutions due to the right-half plane zeros in the hub-torque-to-tip transfer functions. Extending this method to the nonlinear multi-flexible-link case was of particular importance to robotics. When combined with passive joint control in a collaborative effort with a control group, Bayo's inverse dynamics approach led to exponentially-stable tip tracking control for flexible multi-link robots.
Similarly, inverse dynamics in biomechanics computes the net turning effect of all the anatomical structures across a joint, in particular the muscles and ligaments, necessary to produce the observed motions of the joint. These moments of force may then be used to compute the amount of mechanical work
performed by that moment of force. Each moment of force can perform positive work to increase the speed and/or height of the body or perform negative work to decrease the speed and/or height of the body. The equations of motion necessary for these computations are based on Newtonian mechanics, specifically the Newton–Euler equations of:
These equations mathematically model the behaviour of a limb in terms of a knowledge domain-independent, link-segment model, such as idealized solids of revolution
or a skeleton with fixed-length limbs and perfect pivot joints. From these equations, inverse dynamics derives the torque (moment) level at each joint based on the movement of the attached limb or limbs affected by the joint. This process used to derive the joint moments is known as inverse dynamics because it reverses the forward dynamics equations of motion, the set of differential equations which yield the position and angle trajectories of the idealized skeleton's limbs from the accelerations and forces applied.
From joint moments, a biomechanist could infer muscle forces that would lead to those moments based on a model of bone and muscle attachments, etc., thereby estimating muscle activation from kinematic motion.
Correctly computing force (or moment) values from inverse dynamics can be challenging because external forces (e.g., ground contact forces) affect motion but are not directly observable from the kinematic motion. In addition, co-activation of muscles can lead
to a family of solutions which are not distinguishable from the kinematic motion's characteristics. Furthermore, closed kinematic chains, such as swinging a bat or shooting a hockey puck, require the measurement of internal forces (in the bat or stick) be made before shoulder, elbow or wrist moments and forces can be derived.
Inverse problem
An inverse problem is a general framework that is used to convert observed measurements into information about a physical object or system that we are interested in...
. It commonly refers to either inverse rigid body dynamics or inverse structural dynamics
Structural Dynamics
Structural dynamics is a subset of structural analysis which covers the behaviour of structures subjected to dynamic loading. Dynamic loads include people, wind, waves, traffic, earthquakes, and blasts. Any structure can be subject to dynamic loading. Dynamic analysis can be used to find dynamic...
. Inverse rigid-body dynamics is a method for computing forces and/or moments of force (torques) based on the kinematics
Kinematics
Kinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
(motion) of a body and the body's inertial properties (mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
and moment of inertia
Moment of inertia
In classical mechanics, moment of inertia, also called mass moment of inertia, rotational inertia, polar moment of inertia of mass, or the angular mass, is a measure of an object's resistance to changes to its rotation. It is the inertia of a rotating body with respect to its rotation...
). Typically it uses link-segment models to represent the mechanical behaviour of interconnected segments, such as the limb
Limb (anatomy)
A limb is a jointed, or prehensile , appendage of the human or other animal body....
s of humans, animals or robot
Robot
A robot is a mechanical or virtual intelligent agent that can perform tasks automatically or with guidance, typically by remote control. In practice a robot is usually an electro-mechanical machine that is guided by computer and electronic programming. Robots can be autonomous, semi-autonomous or...
s, where given the kinematics of the various parts, inverse dynamics derives the minimum forces and moments responsible for the individual movements. In practice, inverse dynamics computes these internal moments and forces from measurements of the motion of limbs and external forces such as ground reaction force
Ground reaction force
In physics, and in particular in biomechanics, the ground reaction force is the force exerted by the ground on a body in contact with it.For example, a person standing on the ground exerts a contact force on it and at the same time an equal and opposite ground reaction force is exerted by the...
s, under a special set of assumptions.
Applications
The fields of roboticsRobotics
Robotics is the branch of technology that deals with the design, construction, operation, structural disposition, manufacture and application of robots...
and biomechanics
Biomechanics
Biomechanics is the application of mechanical principles to biological systems, such as humans, animals, plants, organs, and cells. Perhaps one of the best definitions was provided by Herbert Hatze in 1974: "Biomechanics is the study of the structure and function of biological systems by means of...
constitute the major application areas for inverse dynamics.
Within robotics
Robotics
Robotics is the branch of technology that deals with the design, construction, operation, structural disposition, manufacture and application of robots...
, inverse dynamics algorithms are used to calculate the torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....
s that a robot's motors must deliver to make the robot's end-point move in the way prescribed by its current task. The "inverse dynamics problem" in Robotics Engineering was solved by Eduardo Bayo
Eduardo Bayo
Eduardo Bayo is a dynamicist known for his work within robotics engineering while a Full Professor at the Department of Mechanical Engineering at UC Santa Barbara....
in 1987. This solution calculates how each of the numerous electric motors that control a robot arm must move to produce a particular action. Humans can perform very complicated and precise movements, such as controlling the tip of a fishing rod well enough to cast the bait accurately. Before the arm moves, the brain calculates the necessary movement of each muscle involved and tells the muscles what to do as the arm swings. In the case of a robot arm, the "muscles" are the electric motors which must turn by a given amount at a given moment. Each motor must be supplied with just the right amount of electrical current, at just the right time. Researchers can predict the motion of a robot arm if they know how the motors will move. This is known as the forward dynamics problem. Until this discovery, they had not been able to work backwards to calculate the movements of the motors required to generate a particular complicated motion., Bayo's work began with the application of frequency-domain methods to the inverse dynamics of single-link flexible robots. This approach yielded non-causal exact solutions due to the right-half plane zeros in the hub-torque-to-tip transfer functions. Extending this method to the nonlinear multi-flexible-link case was of particular importance to robotics. When combined with passive joint control in a collaborative effort with a control group, Bayo's inverse dynamics approach led to exponentially-stable tip tracking control for flexible multi-link robots.
Similarly, inverse dynamics in biomechanics computes the net turning effect of all the anatomical structures across a joint, in particular the muscles and ligaments, necessary to produce the observed motions of the joint. These moments of force may then be used to compute the amount of mechanical work
Mechanical work
In physics, work is a scalar quantity that can be described as the product of a force times the distance through which it acts, and it is called the work of the force. Only the component of a force in the direction of the movement of its point of application does work...
performed by that moment of force. Each moment of force can perform positive work to increase the speed and/or height of the body or perform negative work to decrease the speed and/or height of the body. The equations of motion necessary for these computations are based on Newtonian mechanics, specifically the Newton–Euler equations of:
- ForceForceIn physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
equal massMassMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
times linearLinearIn mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...
accelerationAccelerationIn physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...
, and - MomentMoment (physics)In physics, the term moment can refer to many different concepts:*Moment of force is the tendency of a force to twist or rotate an object; see the article torque for details. This is an important, basic concept in engineering and physics. A moment is valued mathematically as the product of the...
equals mass moment of inertiaMoment of inertiaIn classical mechanics, moment of inertia, also called mass moment of inertia, rotational inertia, polar moment of inertia of mass, or the angular mass, is a measure of an object's resistance to changes to its rotation. It is the inertia of a rotating body with respect to its rotation...
times angular accelerationAngular accelerationAngular acceleration is the rate of change of angular velocity over time. In SI units, it is measured in radians per second squared , and is usually denoted by the Greek letter alpha .- Mathematical definition :...
.
These equations mathematically model the behaviour of a limb in terms of a knowledge domain-independent, link-segment model, such as idealized solids of revolution
Solid of revolution
In mathematics, engineering, and manufacturing, a solid of revolution is a solid figure obtained by rotating a plane curve around some straight line that lies on the same plane....
or a skeleton with fixed-length limbs and perfect pivot joints. From these equations, inverse dynamics derives the torque (moment) level at each joint based on the movement of the attached limb or limbs affected by the joint. This process used to derive the joint moments is known as inverse dynamics because it reverses the forward dynamics equations of motion, the set of differential equations which yield the position and angle trajectories of the idealized skeleton's limbs from the accelerations and forces applied.
From joint moments, a biomechanist could infer muscle forces that would lead to those moments based on a model of bone and muscle attachments, etc., thereby estimating muscle activation from kinematic motion.
Correctly computing force (or moment) values from inverse dynamics can be challenging because external forces (e.g., ground contact forces) affect motion but are not directly observable from the kinematic motion. In addition, co-activation of muscles can lead
to a family of solutions which are not distinguishable from the kinematic motion's characteristics. Furthermore, closed kinematic chains, such as swinging a bat or shooting a hockey puck, require the measurement of internal forces (in the bat or stick) be made before shoulder, elbow or wrist moments and forces can be derived.
See also
- KinematicsKinematicsKinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
- Inverse kinematicsInverse kinematicsInverse kinematics is a subdomain of kinematics, which is of particular interest in robotics and computer animation. In contrast to forward kinematics, which calculates the position of a body after a series of motions, inverse kinematics calculates the motions necessary to achieve a desired...
: a problem similar to Inverse dynamics but with different goals and starting assumptions. While inverse dynamics asks for torques that produce a certain time-trajectory of positions and velocities, inverse kinematics only asks for a static set of joint angles such that a certain point (or a set of points) of the character (or robot) is positioned at a certain designated location. It is used in synthesizing the appearance of human motion, particularly in the field of video game design. Another use is in robotics, where joint angles of an arm must be calculated from the desired position of the end effector. - Body segment parameters
External links
- Inverse dynamics Chris Kirtley's research roundup and tutorials on biomechanical aspects of human gait.