The Sequential Linear Quadratic (SLQ) algorithm is a continuous-time variant\nof the well-known Differential Dynamic Programming (DDP) technique with a\nGauss-Newton Hessian approximation. This family of methods has gained\npopularity in the robotics community due to its efficiency in solving complex\ntrajectory optimization problems. However, one major drawback of DDP-based\nformulations is their inability to properly incorporate path constraints. In\nthis paper, we address this issue by devising a constrained SLQ algorithm that\nhandles a mixture of constraints with a previously implemented projection\ntechnique and a new augmented-Lagrangian approach. By providing an appropriate\nmultiplier update law, and by solving a single inner and outer loop iteration,\nwe are able to retrieve suboptimal solutions at rates suitable for real-time\nmodel-predictive control applications. We particularly focus on the\ninequality-constrained case, where three augmented-Lagrangian penalty functions\nare introduced, along with their corresponding multiplier update rules. These\nare then benchmarked against a relaxed log-barrier formulation in a cart-pole\nswing up example, an obstacle-avoidance task, and an object-pushing task with a\nquadrupedal mobile manipulator.\n