Faster Algorithms for Growing Collision-Free Convex Polytopes in Robot Configuration Space

We propose two novel algorithms for constructing convex collision-free polytopes in robot configuration space. Finding these polytopes enables the application of stronger motion-planning frameworks such as trajectory optimization with Graphs of Convex Sets [1] and is currently a major roadblock in the adoption of these approaches. In this paper, we build upon IRIS-NP (Iterative Regional Inflation by Semidefinite & Nonlinear Programming) [2] to significantly improve tunability, runtimes, and scaling to complex environments. IRIS-NP uses nonlinear programming paired with uniform random initialization to find configurations on the boundary of the free configuration space. Our key insight is that finding near-by configuration-space obstacles using sampling is inexpensive and greatly accelerates region generation. We propose two algorithms using such samples to either employ nonlinear programming more efficiently (IRIS-NP2 ) or circumvent it altogether using a massively-parallel zero-order optimization strategy (IRIS-ZO). We also propose a termination condition that controls the probability of exceeding a user-specified permissible fraction-in-collision, eliminating a significant source of tuning difficulty in IRIS-NP. We compare performance across eight robot environments, showing that IRIS-ZO achieves an order-of-magnitude speed advantage over IRIS-NP. IRISNP2, also significantly faster than IRIS-NP, builds larger polytopes using fewer hyperplanes, enabling faster downstream computation. Website: https://sites.google.com/view/fastiris

Growing Q-Networks: Solving Continuous Control Tasks with Adaptive Control Resolution

Recent reinforcement learning approaches have shown surprisingly strong capabilities of bang-bang policies for solving continuous control benchmarks. The underlying coarse action space discretizations often yield favourable exploration characteristics while final performance does not visibly suffer in the absence of action penalization in line with optimal control theory. In robotics applications, smooth control signals are commonly preferred to reduce system wear and energy efficiency, but action costs can be detrimental to exploration during early training. In this work, we aim to bridge this performance gap by growing discrete action spaces from coarse to fine control resolution, taking advantage of recent results in decoupled Q-learning to scale our approach to high-dimensional action spaces up to dim(A) = 38. Our work indicates that an adaptive control resolution in combination with value decomposition yields simple critic-only algorithms that yield surprisingly strong performance on continuous control tasks.

Certifying Bimanual RRT Motion Plans in a Second

We present an efficient method for certifying non-collision for piecewise-polynomial motion plans in algebraic reparametrizations of configuration space. Such motion plans include those generated by popular randomized methods including RRTs and PRMs, as well as those generated by many methods in trajectory optimization. Based on Sums-of-Squares optimization, our method provides exact, rigorous certificates of non-collision; it can never falsely claim that a motion plan containing collisions is collision-free. We demonstrate that our formulation is practical for real world deployment, certifying the safety of a twelve degree of freedom motion plan in just over a second. Moreover, the method is capable of discriminating the safety or lack thereof of two motion plans which differ by only millimeters.

Approximating Robot Configuration Spaces with few Convex Sets using Clique Covers of Visibility Graphs

Many computations in robotics can be dramatically accelerated if the robot configuration space is described as a collection of simple sets. For example, recently developed motion planners rely on a convex decomposition of the free space to design collision-free trajectories using fast convex optimization. In this work, we present an efficient method for approximately covering complex configuration spaces with a small number of polytopes. The approach constructs a visibility graph using sampling and generates a clique cover of this graph to find clusters of samples that have mutual line of sight. These clusters are then inflated into large, full-dimensional, polytopes. We evaluate our method on a variety of robotic systems and show that it consistently covers larger portions of free configuration space, with fewer polytopes, and in a fraction of the time compared to previous methods.

Certified Polyhedral Decompositions of Collision-Free Configuration Space

Understanding the geometry of collision-free configuration space (C-free) in the presence of task-space obstacles is an essential ingredient for collision-free motion planning. While it is possible to check for collisions at a point using standard algorithms, to date no practical method exists for computing C-free regions with rigorous certificates due to the complexity of mapping task-space obstacles through the kinematics. In this work, we present the first to our knowledge rigorous method for approximately decomposing a rational parametrization of C-free into certified polyhedral regions. Our method, called C-IRIS (C-space Iterative Regional Inflation by Semidefinite programming), generates large, convex polytopes in a rational parameterization of the configuration space which are rigorously certified to be collision-free. Such regions have been shown to be useful for both optimization-based and randomized motion planning. Based on convex optimization, our method works in arbitrary dimensions, only makes assumptions about the convexity of the obstacles in the task space, and is fast enough to scale to realistic problems in manipulation. We demonstrate our algorithm's ability to fill a non-trivial amount of collision-free C-space in several 2-DOF examples where the C-space can be visualized, as well as the scalability of our algorithm on a 7-DOF KUKA iiwa, a 6-DOF UR3e and 12-DOF bimanual manipulators. An implementation of our algorithm is open-sourced in Drake. We furthermore provide examples of our algorithm in interactive Python notebooks.

Solving Continuous Control via Q-learning

While there has been substantial success in applying actor-critic methods to continuous control, simpler critic-only methods such as Q-learning often remain intractable in the associated high-dimensional action spaces. However, most actor-critic methods come at the cost of added complexity: heuristics for stabilization, compute requirements as well as wider hyperparameter search spaces. We show that these issues can be largely alleviated via Q-learning by combining action discretization with value decomposition, framing single-agent control as cooperative multi-agent reinforcement learning (MARL). With bang-bang actions, performance of this critic-only approach matches state-of-the-art continuous actor-critic methods when learning from features or pixels. We extend classical bandit examples from cooperative MARL to provide intuition for how decoupled critics leverage state information to coordinate joint optimization, and demonstrate surprisingly strong performance across a wide variety of continuous control tasks.

Finding and Optimizing Certified, Collision-Free Regions in Configuration Space for Robot Manipulators

Configuration space (C-space) has played a central role in collision-free motion planning, particularly for robot manipulators. While it is possible to check for collisions at a point using standard algorithms, to date no practical method exists for computing collision-free C-space regions with rigorous certificates due to the complexities of mapping task-space obstacles through the kinematics. In this work, we present the first to our knowledge method for generating such regions and certificates through convex optimization. Our method, called C-Iris (C-space Iterative Regional Inflation by Semidefinite programming), generates large, convex polytopes in a rational parametrization of the configuration space which are guaranteed to be collision-free. Such regions have been shown to be useful for both optimization-based and randomized motion planning. Our regions are generated by alternating between two convex optimization problems: (1) a simultaneous search for a maximal-volume ellipse inscribed in a given polytope and a certificate that the polytope is collision-free and (2) a maximal expansion of the polytope away from the ellipse which does not violate the certificate. The volume of the ellipse and size of the polytope are allowed to grow over several iterations while being collision-free by construction. Our method works in arbitrary dimensions, only makes assumptions about the convexity of the obstacles in the task space, and scales to realistic problems in manipulation. We demonstrate our algorithm's ability to fill a non-trivial amount of collision-free C-space in a 3-DOF example where the C-space can be visualized, as well as the scalability of our algorithm on a 7-DOF KUKA iiwa and a 12-DOF bimanual manipulator.

Vision-Based Proprioceptive Sensing for Soft Inflatable Actuators

This paper presents a vision-based sensing approach for a soft linear actuator, which is equipped with an integrated camera. The proposed vision-based sensing pipeline predicts the three-dimensional position of a point of interest on the actuator. To train and evaluate the algorithm, predictions are compared to ground truth data from an external motion capture system. An off-the-shelf distance sensor is integrated in a similar actuator and its performance is used as a baseline for comparison. The resulting sensing pipeline runs at 40 Hz in real-time on a standard laptop and is additionally used for closed loop elongation control of the actuator. It is shown that the approach can achieve comparable accuracy to the distance sensor.