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Hippo: High-performance Interior-Point and Projection-based Solver for Generic Constrained Trajectory Optimization

Haizhou Zhao, Ludovic Righetti, Majid Khadiv

TL;DR

Hippo is introduced, a solver that can handle inequality constraints using the interior-point method (IPM) with an adaptive barrier update strategy and hard equality constraints via projection or IPM and is shown to be a robust and efficient alternative to existing state-of-the-art solvers for difficult robotic trajectory optimization problems requiring high-quality solutions.

Abstract

Trajectory optimization is the core of modern model-based robotic control and motion planning. Existing trajectory optimizers, based on sequential quadratic programming (SQP) or differential dynamic programming (DDP), are often limited by their slow computation efficiency, low modeling flexibility, and poor convergence for complex tasks requiring hard constraints. In this paper, we introduce Hippo, a solver that can handle inequality constraints using the interior-point method (IPM) with an adaptive barrier update strategy and hard equality constraints via projection or IPM. Through extensive numerical benchmarks, we show that Hippo is a robust and efficient alternative to existing state-of-the-art solvers for difficult robotic trajectory optimization problems requiring high-quality solutions, such as locomotion and manipulation.

Hippo: High-performance Interior-Point and Projection-based Solver for Generic Constrained Trajectory Optimization

TL;DR

Hippo is introduced, a solver that can handle inequality constraints using the interior-point method (IPM) with an adaptive barrier update strategy and hard equality constraints via projection or IPM and is shown to be a robust and efficient alternative to existing state-of-the-art solvers for difficult robotic trajectory optimization problems requiring high-quality solutions.

Abstract

Trajectory optimization is the core of modern model-based robotic control and motion planning. Existing trajectory optimizers, based on sequential quadratic programming (SQP) or differential dynamic programming (DDP), are often limited by their slow computation efficiency, low modeling flexibility, and poor convergence for complex tasks requiring hard constraints. In this paper, we introduce Hippo, a solver that can handle inequality constraints using the interior-point method (IPM) with an adaptive barrier update strategy and hard equality constraints via projection or IPM. Through extensive numerical benchmarks, we show that Hippo is a robust and efficient alternative to existing state-of-the-art solvers for difficult robotic trajectory optimization problems requiring high-quality solutions, such as locomotion and manipulation.
Paper Structure (21 sections, 1 theorem, 28 equations, 2 figures, 6 tables, 1 algorithm)

This paper contains 21 sections, 1 theorem, 28 equations, 2 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Main Contribution
  4. Constrained Optimal Control
  5. Riccati Recursion
  6. Intermediate stages
  7. Terminal node
  8. Projection-based Factorization
  9. Value Function Derivative Propagation
  10. Linear Forward Rollout
  11. Sparsity-Preserving Constraint Handling
  12. Regularized Primal-Dual Interior Point Method
  13. Adaptive Barrier Strategy
  14. Iterative Refinement
  15. Fixed-size Backtracking Line Search
  16. ...and 6 more sections

Key Result

Theorem 1

Assuming non-negativeness of $\mathbf{t},\boldsymbol{\nu}$, the regularization term guarantees bounded Hessian modification eq:ipm_q_derivative_increment. Furthermore, assuming $\mathbf{r}_s\approx\mathbf{0}$, the Jacobian modification eq:jacobian_mod_ipm will not explode numerically.

Figures (2)

  • Figure 1: UR5 random SE3 reaching benchmark results. Left plot is the number of sucess v.s. the wall time. Right plot shows the number of QP iterations distribution of the tests.
  • Figure 2: Go2 2-step locomotion benchmark results. 100 random trials are tested for each setting. Missing solver data for a setting indicates that the solver failed all tests for that setting.

Theorems & Definitions (4)

  • Remark 1
  • Remark 2
  • Theorem 1
  • proof