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1. Uncertainty-Aware Constraint Learning for Adaptive Safe Motion Planning from Demonstrations

   Chou, Glen; Ozay, Necmiye; Berenson, Dmitry (January 2020, Conference on Robot Learning)

   null (Ed.)

   We present a method for learning to satisfy uncertain constraints fromdemonstrations. Our method uses robust optimization to obtain a belief over thepotentially infinite set of possible constraints consistent with the demonstrations,and then uses this belief to plan trajectories that trade off performance with sat-isfying the possible constraints. We use these trajectories in a closed-loop policythat executes and replans using belief updates, which incorporate data gatheredduring execution. We derive guarantees on the accuracy of our constraint beliefand probabilistic guarantees on plan safety. We present results on a 7-DOF armand 12D quadrotor, showing our method can learn to satisfy high-dimensional (upto 30D) uncertain constraints, and outperforms baselines in safety and efficiency. 

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2. Tuning-Free Contact-Implicit Trajectory Optimization

   Onol, Aykut O; Corcodel, R; Long, P; Padir, T. (January 2020, IEEE International Conference on Robotics and Automation)

   We present a contact-implicit trajectory optimization framework that can plan contact-interaction trajectories for different robot architectures and tasks using a trivial initial guess and without requiring any parameter tuning. This is achieved by using a relaxed contact model along with an automatic penalty adjustment loop for suppressing the relaxation. Moreover, the structure of the problem enables us to exploit the contact information implied by the use of relaxation in the previous iteration, such that the solution is explicitly improved with little computational overhead. We test the proposed approach in simulation experiments for non-prehensile manipulation using a 7-DOF arm and a mobile robot and for planar locomotion using a humanoid-like robot in zero gravity. The results demonstrate that our method provides an out-of-the-box solution with good performance for a wide range of applications. 

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3. Efficient Computation of Higher-Order Variational Integrators in Robotic Simulation and Trajectory Optimization

   https://doi.org/10.1007/978-3-030-44051-0_40  

   Fan, T.; Schultz, J.; Murphey, T. (May 2020, Workshop on the Algorithmic Foundations of Robotics)

   This paper addresses the problem of efficiently computing higher- order variational integrators in simulation and trajectory optimization of mechanical systems as those often found in robotic applications. We develop O(n) algorithms to evaluate the discrete Euler-Lagrange (DEL) equations and compute the Newton direction for solving the DEL equations, which results in linear-time variational integrators of arbitrarily high order. To our knowledge, no linear-time higher-order variational or even implicit integrators have been developed before. Moreover, an O(n2) algorithm to linearize the DEL equations is presented, which is useful for trajectory optimization. These proposed algorithms eliminate the bottleneck of implementing higher-order variational integrators in simulation and trajectory optimization of complex robotic systems. The efficacy of this paper is validated through comparison with existing methods, and implementation on various robotic systems—including trajectory optimization of the Spring Flamingo robot, the LittleDog robot and the Atlas robot. The results illustrate that the same integrator can be used for simulation and trajectory optimization in robotics, preserving mechanical properties while achieving good scalability and accuracy. 

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4. Motion Planning around Obstacles with Convex Optimization

   Tobia Marcucci, Mark Petersen2 (May 2022, ArXivorg)

   Trajectory optimization o↵ers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to sampling-based planners that struggle in very high dimensions and with continuous di↵erential constraints. Indeed, obstacles are the source of many textbook examples of problematic nonconvexities in the trajectory-optimization prob- lem. Here we show that convex optimization can, in fact, be used to reliably plan trajectories around obstacles. Specifically, we consider planning problems with collision-avoidance constraints, as well as cost penalties and hard constraints on the shape, the duration, and the velocity of the trajectory. Combining the properties of B ́ezier curves with a recently-proposed framework for finding shortest paths in Graphs of Convex Sets (GCS), we formulate the planning problem as a compact mixed-integer optimization. In stark contrast with existing mixed-integer planners, the convex relaxation of our programs is very tight, and a cheap round- ing of its solution is typically sufficient to design globally-optimal trajectories. This reduces the mixed-integer program back to a simple convex optimization, and automatically provides optimality bounds for the planned trajectories. We name the proposed planner GCS, after its underlying optimization framework. We demonstrate GCS in simulation on a variety of robotic platforms, including a quadrotor flying through buildings and a dual-arm manipulator (with fourteen degrees of freedom) moving in a confined space. Using numerical experiments on a seven-degree-of-freedom manipulator, we show that GCS can outperform widely-used sampling-based planners by finding higher-quality trajectories in less time. 

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5. Contact-Implicit Optimization of Locomotion Trajectories for a Quadrupedal Microrobot

   https://doi.org/10.15607/RSS.2018.XIV.041  

   Doshi, Neel; Jayaram, Kaushik; Goldberg, Benjamin; Manchester, Zachary; Wood, Robert; Kuindersma, Scott (June 2018, Robotics: Science and Systems)

   Planning locomotion trajectories for legged microrobots is challenging. This is because of their complex morphology, high frequency passive dynamics, and discontinuous contact interactions with their environment. Consequently, such research is often driven by time-consuming experimental methods. As an alternative, we present a framework for systematically modeling, planning, and controlling legged microrobots. We develop a three- dimensional dynamic model of a 1.5 g quadrupedal microrobot with complexity (e.g., number of degrees of freedom) similar to larger-scale legged robots. We then adapt a recently developed variational contact-implicit trajectory optimization method to generate feasible whole-body locomotion plans for this microrobot, and demonstrate that these plans can be tracked with simple joint-space controllers. We plan and execute periodic gaits at multiple stride frequencies and on various surfaces. These gaits achieve high per-cycle velocities, including a maximum of 10.87 mm/cycle, which is 15% faster than previously measured for this microrobot. Furthermore, we plan and execute a vertical jump of 9.96 mm, which is 78% of the microrobot’s center-of- mass height. To the best of our knowledge, this is the first end-to-end demonstration of planning and tracking whole-body dynamic locomotion on a millimeter-scale legged microrobot. 

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