Robust Trajectory Optimization Under Frictional Contact with Iterative Learning

Abstract

Abstract-Optimization is often difficult to apply to robots due to the presence of modeling errors, which may cause constraints to be violated during execution on a real robot. This work presents a method to optimize trajectories with large modeling errors using a combination of robust optimization and parameter learning. In particular it considers the problem of computing a dynamically-feasible trajectory along a fixed path under frictional contact, where friction is uncertain and actuator effort is noisy. It introduces a robust time-scaling method that is able to accept confidence intervals on uncertain parameters, and uses a convex parameterization that allows dynamically-feasible motions under contact to be computed in seconds. This is combined with an iterative learning method that uses feedback from execution to learn confidence bounds on modeling parameters. Experiments on a manipulator performing a "waiter" task, on which an object is moved on a carried tray as quickly as possible, demonstrate this method can compensate for modeling uncertainties within a handful of iterations.

Critically fast pick-and-place with suction cups

“…Similar to the classical ZMP concept for humanoid locomotion, this approach has two limitations: (i) it can only be applied if the object is on a flat surface and (ii) there is no guarantee that the object does not slip or twist [20]. In a more recent work [21], Luo and Hauser proposed to consider the individual contact forces explicitly, eliminating the use of the ZMP and its limitations. However, their formulation resulted in a non-convex non-linear optimization problem that is computationally demanding, taking several seconds to terminate.…”

Robustness to joint-torque-tracking errors in task-space inverse dynamics

“…Mordatch et al [53] considered several perturbed models of a humanoid robot to plan offline a trajectory that is robust to uncertainties, reporting success rate between 80% and 95% on a real platform. Another recent work [54] has combined robust and timescaling optimization to plan trajectories that are robust to bounded errors in friction coefficients and joint accelerations, whose magnitude can be estimated online through iterative learning. Finally, Nguyen and Sreenath [55] have recently exploited control Lyapunov functions and QPs to ensure stability despite bounded uncertainties in the linearized system dynamics.…”

“…For instance, the same approaches presented here could be applied to Model Predictive Control (MPC), a control technique that has become ubiquitous in robotics for the generation of walking motion [43], [52]. While robust MPC is already an active research field [60]- [62], applications of robust optimization in robotics are seldom [54], [55], [63], [64].…”

Unknown External Force Estimation and Collision Detection for a Cooperative Robot

“…3 This approach is named pure position control; pure position control is inadequate or even unstable for tasks that involve motions in uncertain environments. 4,5 Since accidental collisions are probable when a robot is intended to work alongside an operator, force control is needed. Force control demands supervision of external forces exerted on the manipulator, 6 which can be accomplished with external sensors such as capacitive skin 7 or force sensors.…”