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, sound source reconstruction, source reconstruction in ac ...

. 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 In physics, kinematics studies the geometrical aspects of motion of physical objects independent of forces that set them in motion. Constrained motion such as linked machine parts are also described as kinematics. Kinematics is concerned with s ...

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

mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...

and

moment of inertia The moment of inertia, otherwise known as the mass moment of inertia, angular/rotational mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is defined relatively to a rotational axis. It is the ratio between ...

). Typically it uses link-segment models to represent the mechanical behaviour of interconnected segments, such as the limbs of humans or animals or the joint extensions of

robot A robot is a machine—especially one Computer program, programmable by a computer—capable of carrying out a complex series of actions Automation, automatically. A robot can be guided by an external control device, or the robot control, co ...

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 per ...

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 the interdisciplinary study and practice of the design, construction, operation, and use of robots. Within mechanical engineering, robotics is the design and construction of the physical structures of robots, while in computer s ...

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 Organ (anatomy), organs, Cell (biology), cells and cell organelles, using the methods of mechani ...

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 analogue of linear force. It is also referred to as the moment of force (also abbreviated to moment). The symbol for torque is typically \boldsymbol\tau, the lowercase Greek letter ''tau''. Wh ...

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" for robotics 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. 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 science, 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 stre ...

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 physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body r ...

, specifically the Newton–Euler equations of: : ''

Force In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...

equal

times

linear In mathematics, the term ''linear'' is used in two distinct senses for two different properties: * linearity of a '' function'' (or '' mapping''); * linearity of a '' polynomial''. An example of a linear function is the function defined by f(x) ...

acceleration In mechanics, acceleration is the Rate (mathematics), rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are Euclidean vector, vector ...

,'' and : '' Moment equals mass moment of inertia times

angular acceleration In physics, angular acceleration (symbol α, alpha) is the time rate of change of angular velocity. Following the two types of angular velocity, ''spin angular velocity'' and ''orbital angular velocity'', the respective types of angular accele ...

''. These equations mathematically model the behavior 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.

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