Trajectory tracking is the control problem of causing a dynamical system—typically a robot, vehicle, or aerial platform—to follow a prescribed time-parameterised path through configuration space with minimal deviation. It couples a reference trajectory generated by a planner with a feedback controller that corrects errors arising from disturbances, model mismatch, and actuation limits. Trajectory tracking controllers range from classical PID and linear quadratic regulators to model predictive controllers and learning-based approaches. It is a central capability in mobile robotics, autonomous driving, drone flight, and industrial manipulator control.
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- Trajectory tracking sits at the intersection of planning and control. A planner generates a desired trajectory—a sequence of states with associated times—that respects kinematic and dynamic constraints. The tracking controller then computes actuation commands at each control cycle to minimise the error between the robot’s actual state and the desired state on the reference trajectory, handling the inevitable discrepancy caused by disturbances, friction, and model inaccuracy.
- Classical linear controllers such as PID regulators can achieve adequate tracking performance on slow, near-linear systems. For higher-speed or more complex dynamics, linear quadratic regulators (LQR) and model predictive controllers (MPC) provide better performance by exploiting an explicit system model and optimising over a receding horizon. MPC is particularly valuable because it naturally handles actuator saturation, state constraints, and multi-variable coupling in a unified optimisation framework.
- Legged robots and aerial vehicles pose especially challenging trajectory tracking problems because their dynamics are highly non-linear, have underactuated degrees of freedom, and operate with significant contact-event discontinuities. Whole-body control frameworks and differential-flatness-based feedforward terms combined with robust feedback have become the state of the art for high-performance legged locomotion and drone aerobatics.
- Learning-based approaches—neural network policies trained via imitation learning or reinforcement learning—are increasingly competitive with model-based controllers for tracking complex trajectories, particularly in domains where system identification is expensive. Hybrid architectures that combine learned residual models with classical control structures offer the best of both worlds: stability guarantees from the model-based backbone and adaptability from the learned component.