This thesis studies Imitation Learning under constraints. A demonstration shows desirable behaviour, not necessarily admissible behaviour --- the reproduced motion may violate the robot's kinematics, or it may conflict with a scene the demonstrator did not anticipate. The two classes of constraint, intrinsic ones due to the robot's kinematics and extrinsic ones due to the workspace and the scene, motivate two technical contributions built on the structured representations that suit the small-data regime: Dynamic Movement Primitives (DMPs) and Task-Parameterised Gaussian Mixture Models (TP-GMMs). Both contributions arise from a unified Hilbert-norm reading of the two families as instances of the same constrained optimisation template. The DMP generalisation in this reading assumes a linear admissible-trajectory set, an assumption that fails under nonholonomic kinematics, and the thesis introduces Nonholonomic Dynamic Movement Primitives (NHDMPs), built on a quasi-velocity reformulation of trajectory imitation, to encode the kinematic constraint by construction. TP-GMM captures scene dependence through rigid relocation of task frames; the thesis prepends a scene-conditioned correction stage that adapts the trajectory before execution to scene features beyond the task-frame parametrisation. Two learned heads, trained on a small set of labelled scene variations, predict whether correction is needed and in which direction it must act; the correction magnitude is read from the TP-GMM covariance, without retraining the underlying skill. NHDMPs are benchmarked against the numerical solution of the constrained imitation problem, validated on the unicycle model and on the AlterEgo robot, and extended to car-like vehicles. The correction stage is validated on a planar collision-avoidance task and on a three-dimensional picking task with a Franka manipulator. The thesis closes with a discussion that compares the two contributions, draws connections with biological motor control, and reports collaborative work that deployed the AlterEgo platform within a motor-imagery brain--computer-interface pipeline and within artistic performances.