ALTRO: A Fast Solver for Constrained Trajectory Optimization Trajectory optimization is a widely used tool for robot motion planning and control. Existing solvers for these problems either rely on offtheshelf nonlinear programming solvers that are numerically robust and capable of handling arbitrary constraints, but tend to be slow because they are general purpose; or they use custom numerical methods that take advantage of the problem structure to be fast, but often lack robustness and have limited or no ability to reason about constraints. This paper presents ALTRO (Augmented Lagrangian TRajectory optimizer), a solver for constrained trajectory optimization problems that handles general nonlinear state and input constraints and offers fast convergence and numerical robustness thanks to careful exploitation of problem structure. We demonstrate its performance on a set of benchmark motionplanning problems and offer comparisons to the standard direct collocation method with largescale sequential quadratic programming and interiorpoint solvers.

Trajectory Optimization for Unknown Constrained Systems using Reinforcement Learning In this paper, we propose a reinforcement learningbased algorithm for trajectory optimization for constrained dynamical systems. This problem is motivated by the fact that for most robotic systems, the dynamics may not always be known. Generating smooth, dynamically feasible trajectories could be difficult for such systems. Using samplingbased algorithms for motion planning may result in trajectories that are prone to undesirable control jumps. However, they can usually provide a good reference trajectory which a modelfree reinforcement learning algorithm can then exploit by limiting the search domain and quickly finding a dynamically smooth trajectory. We use this idea to train a reinforcement learning agent to learn a dynamically smooth trajectory in a curriculum learning setting. Furthermore, for generalization, we parameterize the policies with goal locations, so that the agent can be trained for multiple goals simultaneously. We show result in both simulated environments as well as real experiments, for a 6DoF manipulator arm operated in positioncontrolled mode to validate the proposed idea. We compare the proposed ideas against a PID controller which is used to track a designed trajectory in configuration space. Our experiments show that our RL agent trained with a reference path outperformed a modelfree PID controller of the type commonly used on many robotic platforms for trajectory tracking.