Every engineer who has worked with robot arms knows the frustration: you tune your controller perfectly for slow movements, then crank up the speed and everything falls apart. The arm overshoots, oscillates, or misses its target entirely. What changed?

The answer lies in robot dynamics—the physics of motion that become impossible to ignore as speeds and payloads increase. A stationary arm only fights gravity. A moving arm contends with inertia, momentum transfer between joints, and velocity-dependent forces that can overwhelm even well-tuned position controllers.

Understanding these dynamic effects transforms how you approach controller design. Instead of treating unexpected behaviors as noise to be suppressed, you can model them precisely and compensate proactively. The result is faster, smoother motion with better tracking accuracy—turning physics from an adversary into an ally.

The mass matrix sits at the heart of robot dynamics. This symmetric, positive-definite matrix describes how much torque each joint motor must produce to accelerate each link—and crucially, how acceleration at one joint creates reaction torques at others.

Consider a two-link arm swinging its elbow while the shoulder holds position. The elbow's acceleration changes the effective moment of inertia seen by the shoulder motor. Without compensation, the shoulder drifts. This inertial coupling becomes more pronounced as link masses increase and as motion speeds up.

The mass matrix also varies with configuration. An arm extended straight outward presents maximum inertia to the shoulder joint. The same arm folded close to the body might require half the torque for identical acceleration. Your controller must account for this configuration-dependent behavior, or performance will vary dramatically across the workspace.

These coupling effects explain why independent joint controllers—treating each axis as a separate SISO system—hit fundamental limits. The physics couples the joints whether you model it or not. Ignoring coupling means your controller constantly fights disturbances that are actually predictable consequences of the arm's own motion.

Takeaway

Robot joints are not independent systems—they form a coupled dynamic network where motion at any joint creates forces throughout the entire mechanism.

Hold your arm straight out from your shoulder. Within seconds, you feel the effort required just to maintain position. Robot arms face this challenge continuously—gravity creates static torques that motors must counteract even when the arm isn't moving.

These gravity torques depend entirely on configuration. A vertical arm segment requires zero gravity compensation. Rotate that segment horizontal, and suddenly the motor fights the full weight times the moment arm. The gravity vector in joint space changes continuously as the robot moves.

Feedforward gravity compensation addresses this predictably. If you know the link masses and centers of gravity, you can calculate exactly what torque each motor needs to counteract gravity at any configuration. Adding this as a feedforward term means your feedback controller only handles deviations from expected behavior, not the entire static load.

The improvement in tracking accuracy can be dramatic. Without gravity compensation, a position controller wastes much of its output just holding position, leaving less authority for actual trajectory following. With proper feedforward, the full controller bandwidth addresses dynamic errors. This is especially critical for precise operations at low speeds, where dynamic effects are small but gravity torque remains constant.

Takeaway

Gravity compensation separates the predictable physics you can calculate from the unpredictable disturbances you must react to—letting your feedback controller focus on what actually matters.

Computed torque control—sometimes called inverse dynamics control—takes feedforward compensation to its logical conclusion. Instead of compensating only for gravity, you calculate and cancel all dynamic effects: inertia, coupling, centrifugal forces, and Coriolis forces.

The approach requires a complete dynamic model of your robot. At each control cycle, you compute what torques the physics demands for the desired acceleration, then add corrections from a feedback controller operating on tracking error. If your model is perfect, the feedback controller sees a simple double-integrator system regardless of the actual robot's complexity.

This linearization through nonlinear control enables powerful analysis and design techniques. Standard linear control methods—pole placement, LQR, PID—work as expected because the computed torque term handles the nonlinearities. You design for the simple system you want, not the complicated system you have.

Model accuracy becomes the critical constraint. Unmodeled friction, actuator dynamics, and parameter errors all degrade performance. Practical implementations often combine computed torque with robust feedback terms that handle modeling uncertainty. Adaptive variants estimate parameters online, continuously refining the dynamic model as the robot operates.

Takeaway

Computed torque control inverts the robot's physics, transforming a complex nonlinear system into something your linear controller can handle cleanly.

Robot dynamics reveals why simple controllers struggle as performance demands increase. The mass matrix, gravity terms, and velocity-dependent forces create behaviors that no amount of gain tuning can fully address without explicit modeling.

Understanding these effects opens the door to model-based control strategies. Feedforward compensation for predictable terms—gravity, inertia, coupling—frees your feedback controller to address genuine disturbances and tracking errors.

The investment in accurate dynamic modeling pays dividends in faster cycle times, smoother trajectories, and better end-effector accuracy. For high-performance applications, the dynamics aren't optional physics to fight—they're the foundation your control strategy builds upon.