Inverse dynamics is an

inverse problem An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the ...

. It commonly refers to either inverse rigid body dynamics or inverse

structural dynamics Structural dynamics is a type of structural analysis which covers the behavior of a structure subjected to dynamic (actions having high acceleration) loading. Dynamic loads include people, wind, waves, traffic, earthquakes, and blasts. Any structur ...

. Inverse

rigid-body dynamics In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are ''rigid'' (i.e. they do not deform under the action ...

is a method for computing forces and/or moments of force (torques) based on the

kinematics Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, Physical object, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause ...

(motion) of a body and the body's inertial properties (

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...

and

moment of inertia The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceler ...

). Typically it uses link-segment models to represent the mechanical behaviour of interconnected segments, such as the

limb Limb may refer to: Science and technology *Limb (anatomy), an appendage of a human or animal *Limb, a large or main branch of a tree *Limb, in astronomy, the curved edge of the apparent disk of a celestial body, e.g. lunar limb *Limb, in botany, ...

s of humans or animals or the joint extensions of

robot A robot is a machine—especially one programmable by a computer—capable of carrying out a complex series of actions automatically. A robot can be guided by an external control device, or the control may be embedded within. Robots may be c ...

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 In physics, and in particular in biomechanics, the ground reaction force (GRF) is the force exerted by the ground on a body in contact with it. For example, a person standing motionless on the ground exerts a contact force on it (equal to the person ...

s, under a special set of assumptions.Robertson DGE, et al., Research Methods in Biomechanics, Champaign IL:Human Kinetics Pubs., 2004.

Applications

The fields of

robotics Robotics is an interdisciplinary branch of computer science and engineering. Robotics involves design, construction, operation, and use of robots. The goal of robotics is to design machines that can help and assist humans. Robotics integrat ...

and

biomechanics Biomechanics is the study of the structure, function and motion of the mechanical aspects of biological systems, at any level from whole organisms to organs, cells and cell organelles, using the methods of mechanics. Biomechanics is a branch of ...

constitute the major application areas for inverse dynamics. Within

, inverse dynamics algorithms are used to calculate the

torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...

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 electric 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.Bayo E., "A Finite Element Approach to Control the End-Point Motion of a Single Link Flexible Robot," "Journal of Robotic Systems", Vol. 4, No. 1, pp. 63–75. Feb. 1987. 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 In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force stren ...

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 Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in motion ...

, specifically the

Newton–Euler equations In classical mechanics, the Newton–Euler equations describe the combined translational and rotational dynamics of a rigid body. Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rig ...

of: : ''

Force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...

equal

times

linear Linearity is the property of a mathematical relationship (''function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear r ...

acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...

,'' and : '' Moment equals

mass moment of inertia The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceler ...

times

angular acceleration In physics, angular acceleration refers to the time rate of change of angular velocity. As there are two types of angular velocity, namely spin angular velocity and orbital angular velocity, there are naturally also two types of angular acceler ...

. 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 In geometry, a solid of revolution is a solid figure obtained by rotating a plane figure around some straight line (the ''axis of revolution'') that lies on the same plane. The surface created by this revolution and which bounds the solid is the ...

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.

References

* *{{cite journal , author=Jensen RK , title=Changes in segment inertia proportions between four and twenty years , journal=Journal of Biomechanics , year=1989 , volume=22 , pages=529–36 , pmid=2808438 , issue=6–7 , doi=10.1016/0021-9290(89)90004-3

External links

Inverse dynamics
Chris Kirtley's research roundup and tutorials on biomechanical aspects of human gait. Robot control Motor control Inverse problems 1987 in robotics

Applications

See also

References

External links