Optimal control is a widely used tool for synthesizing motions and controls for user-defined tasks under physical constraints. A common approach is to formulate it using direct multiple-shooting and then to use off-the-shelf nonlinear programming solvers that can easily handle arbitrary constraints on the controls and states . However, these methodsare not fast enough for many robotics applications such as real-time humanoid motor control . Exploiting the sparse structure of optimal control problem , such as in Differential DynamicProgramming (DDP), has proven to significantly boost the computational efficiency, and recent works have been focused on handling arbitrary constraints. Despite that , DDP has been associated with poor numerical convergence , particularly when considering long time horizons. One of the main reasons is due to system instabilities and poor warm-starting (only controls). This paper presents control-limited Feasibility-driven DDP (Box-FDDP), a solver that incorporates a direct-indirect hybridization of the control-limited DDP algorithm. Concretely, the forward and backward passes handle feasibility and control limits. We showcase the impact and importance of our method on a set of challenging optimal control problems against the Box-DDP and squashing-function approach .
Differential Dynamic Programming (DDP) is an indirect method for trajectory optimization. Its efficiency derives from the exploitation of temporal structure (inherent to optimal control problems) and explicit roll-out/integration of the system dynamics . However, it suffers from numerical instability and, when compared to direct methods, it has limited initialization options (allows initialization of controls, but not of states) and lacks proper handling of control constraints. These limitations are due to the fact that DDP is a single shooting algorithm. In this work, we tackle these issues with a direct-indirect hybridization approach that is primarily driven by the dynamic feasibility of the optimal control problem . Our feasibility search emulates the numerical resolution of a direct transcription problem with only dynamics constraints, namely a multiple shooting formulation. We show that our approach has better numerical convergence than BOX-DDP (a shooting method), and that its convergence rate and runtime performance are competitive with state-of-the-art direct transcription formulations solved using the interior point and active set algorithms available in KNITRO. We further show that our approach decreases the dynamic feasibility error monotonically -- as in state-of-the-art nonlinear programming algorithms. We demonstrate the benefits of our hybrid approach by generating complex and athletic motions for quadruped and humanoid robots .
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Optimal control is a widely used tool for synthesizing motions and controls for user-defined tasks under physical constraints. A common approach is to formulate it using direct multiple-shooting and then to use off-the-shelf nonlinear programming solvers that can easily handle arbitrary constraints on the controls and states
Differential Dynamic Programming (DDP) is an indirect method for trajectory optimization. Its efficiency derives from the exploitation of temporal structure (inherent to optimal control problems) and explicit roll-out/integration of the system dynamics
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these methodsare not fast enough for many robotics applications such as real-time humanoid motor control . Exploiting the sparse structure of
it suffers from numerical instability and, when compared to direct methods, it has limited initialization options (allows initialization of controls, but not of states) and lacks proper handling of control constraints. These limitations are due to the fact that DDP is a single shooting algorithm. In this work, we tackle these issues with a direct-indirect hybridization approach that is primarily driven by the dynamic feasibility of the
R
, such as in Differential DynamicProgramming (DDP), has proven to significantly boost the computational efficiency, and recent works have been focused on handling arbitrary constraints. Despite that , DDP has been associated with poor numerical convergence , particularly when considering long time horizons. One of the main reasons is due to system instabilities and poor warm-starting (only controls). This paper presents control-limited Feasibility-driven DDP (Box-FDDP), a solver that incorporates a direct-indirect hybridization of the control-limited DDP algorithm. Concretely, the forward and backward passes handle feasibility and control limits. We showcase the impact and importance of our method on a set of challenging optimal control problems against the Box-DDP and squashing-function approach
. Our feasibility search emulates the numerical resolution of a direct transcription problem with only dynamics constraints, namely a multiple shooting formulation. We show that our approach has better numerical convergence than BOX-DDP (a shooting method), and that its convergence rate and runtime performance are competitive with state-of-the-art direct transcription formulations solved using the interior point and active set algorithms available in KNITRO. We further show that our approach decreases the dynamic feasibility error monotonically -- as in state-of-the-art nonlinear programming algorithms. We demonstrate the benefits of our hybrid approach by generating complex and athletic motions for quadruped and humanoid robots