Finding Locally Optimal, Collision-Free Trajectories with Sequential Convex Optimization

By John Schulman, Jonathan Ho, Alex X. Lee, Ibrahim Awwal, Henry Bradlow, Pieter Abbeel. Robotics: Science and Systems Conference, 2013

562 citations recorded by the source corpus.

We present a novel approach for incorporating collision avoidance into trajectory optimization as a method of solving robotic motion planning problems. At the core of our approach are (i) A sequential convex optimization procedure, which penalizes collisions with a hinge loss and increases the penalty coefficients in an outer loop as necessary. (ii) An efficient formulation of the no-collisions constraint that directly considers continuous-time safety and enables the algorithm to reliably solve motion planning problems, including problems involving thin and complex obstacles. We benchmarked our algorithm against several other motion planning algorithms, solving a suite of 7-degree-of-freedom (DOF) arm-planning problems and 18-DOF full-body planning problems. We compared against sampling-based planners from OMPL, and we also compared to CHOMP, a leading approach for trajectory optimization. Our algorithm was faster than the alternatives, solved more problems, and yielded higher quality paths. Experimental evaluation on the following additional problem types also confirmed the speed and effectiveness of our approach: (i) Planning foot placements with 34 degrees of freedom (28 joints + 6 DOF pose) of the Atlas humanoid robot as it maintains static stability and has to negotiate environmental constraints. (ii) Industrial box picking. (iii) Real-world motion planning for the PR2 that requires considering all degrees of freedom at the same time.

Subfields: Biomedical Engineering, Computer Vision and Pattern Recognition, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/7f2190eb7395b90fc9691ea513a6221de343fac3

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Citations in the corpus

Optimization as Estimation with Gaussian Processes in Bandit Settings (2015, methodology): “To solve the SQP, we used SNOPT [9].”
No falls, no resets: Reliable humanoid behavior in the DARPA robotics challenge (2015, methodology): “We used both precalculated trajectories and TrajOpt [11] to plan trajectories in real-time.”
A Potential Field-Based Model Predictive Path-Planning Controller for Autonomous Road Vehicles (2017, methodology): “[24] uses the SD between the vehicle shape and the obstacle shape for collision avoidance.”
Learning preferences for manipulation tasks from online coactive feedback (2015, methodology): “Such preferences are often encoded as a cost which planners optimize [26, 50, 63].”
Feature Expansive Reward Learning: Rethinking Human Input (2020, methodology): “We then use TrajOpt [22] to produce optimal trajectories for 100 randomly selected start-goal pairs under the learned rewards.”
Analysis and Observations From the First Amazon Picking Challenge (2016, methodology): “Other tools mentioned by the teams include “trajopt” [22], ROS’ JT Cartesian Controller [23], and the OMPL library [24], which was interfaced through MoveIt! or stand-alone in the teams’ custom implementations.”
Whole-body motion planning with centroidal dynamics and full kinematics (2014, unknown): “use a true hinge-loss function for a similar purpose [22].”
Differentiable Gaussian Process Motion Planning (2019, background): “Trajectory optimization is a powerful approach to effectively solving the planning problem and state-of-the-art algorithms can find smooth, collision free trajectories in almost real-time for complex systems such as robot manipulators [1, 2, 3].”
Motion planning with sequential convex optimization and convex collision checking (2014, methodology): “In this work, in addition to providing a revised and extended version of our work [43], (i) we describe an extension to the algorithm described in the RSS paper to plan trajectories in SE (3) , and (ii) we provide a discussion on cases where trajectory optimization fails to ﬁnd a feasible solution.”
Learning accurate kinematic control of cable-driven surgical robots using data cleaning and Gaussian Process Regression (2014, background): “Further information on this research, including data, code, photos, and video, is available at: http://rll.berkeley.edu/surgical.”
Recent Advances in Robot Learning from Demonstration (2020, methodology): “Traditional trajectory optimization methods (5, 108, 109) were originally introduced to generate smooth and efficient trajectories for robots to move between any two given points in space.”
Neural Autonomous Navigation with Riemannian Motion Policy (2019, background): “The complete knowledge of the geometric structure allows optimal local obstacle avoidance [19] and advanced planning algorithms to perform long-range trajectory optimization [26], [27].”
Learning from Demonstrations Through the Use of Non-rigid Registration (2013, methodology): “We solve this problem using the trajectory optimization method from [21].”
A case study of trajectory transfer through non-rigid registration for a simplified suturing scenario (2013, methodology): “Our experiments consider a simplified suturing scenario, both with a simulated Raven II system [5] and with a real PR2, and show that a single demonstration (provided by a human) can be generalized to a variety of initial conditions.”
Deictic Image Maps: An Abstraction For Learning Pose Invariant Manipulation Policies (2018, methodology): “All end-to-end motions commanded by the agent were planned using TrajOpt (Schulman et al. 2013) with the final gripper pose constrained to be orthogonal to the table.”
Combined task and motion planning through an extensible planner-independent interface layer (2014, background): “Trajopt (multi-init mode), which is a state-of-the-art motion planner that uses sequential convex optimization to compute collision avoiding trajectories [5].”