Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTrajectory optimization for contact-rich motions using implicit differential dynamic programming
222
0
0.0
(
0
)
Added by
Iordanis Chatzinikolaidis
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
This paper presents a novel approach using sensitivity analysis for generalizing Differential Dynamic Programming (DDP) to systems characterized by implicit dynamics, such as those modelled via inverse dynamics and variational or implicit integrators. It leads to a more general formulation of DDP, enabling for example the use of the faster recursive Newton-Euler inverse dynamics. We leverage the implicit formulation for precise and exact contact modelling in DDP, where we focus on two contributions: (1) Contact dynamics in acceleration level that enables high-order integration schemes; (2) Formulation using an invertible contact model in the forward pass and a closed form solution in the backward pass to improve the numerical resolution of contacts. The performance of the proposed framework is validated (1) by comparing implicit versus explicit DDP for the swing-up of a double pendulum, and (2) by planning motions for two tasks using a single leg model making multi-body contacts with the environment: standing up from ground, where a priori contact enumeration is challenging, and maintaining balance under an external perturbation.
rate research
Read More
This paper presents a novel contact-implicit trajectory optimization method using an analytically solvable contact model to enable planning of interactions with hard, soft, and slippery environments. Specifically, we propose a novel contact model that can be computed in closed-form, satisfies friction cone constraints and can be embedded into direct trajectory optimization frameworks without complementarity constraints. The closed-form solution decouples the computation of the contact forces from other actuation forces and this property is used to formulate a minimal direct optimization problem expressed with configuration variables only. Our simulation study demonstrates the advantages over the rigid contact model and a trajectory optimization approach based on complementarity constraints. The proposed model enables physics-based optimization for a wide range of interactions with hard, slippery, and soft grounds in a unified manner expressed by two parameters only. By computing trotting and jumping motions for a quadruped robot, the proposed optimization demonstrates the versatility for multi-contact motion planning on surfaces with different physical properties.
Applying intelligent robot arms in dynamic uncertain environments (i.e., flexible production lines) remains challenging, which requires efficient algorithms for real time trajectory generation. The motion planning problem for robot trajectory generation is highly nonlinear and nonconvex, which usually comes with collision avoidance constraints, robot kinematics and dynamics constraints, and task constraints (e.g., following a Cartesian trajectory defined on a surface and maintain the contact). The nonlinear and nonconvex planning problem is computationally expensive to solve, which limits the application of robot arms in the real world. In this paper, for redundant robot arm planning problems with complex constraints, we present a motion planning method using iterative convex optimization that can efficiently handle the constraints and generate optimal trajectories in real time. The proposed planner guarantees the satisfaction of the contact-rich task constraints and avoids collision in confined environments. Extensive experiments on trajectory generation for weld grinding are performed to demonstrate the effectiveness of the proposed method and its applicability in advanced robotic manufacturing.
We present a framework for bi-level trajectory optimization in which a systems dynamics are encoded as the solution to a constrained optimization problem and smooth gradients of this lower-level problem are passed to an upper-level trajectory optimizer. This optimization-based dynamics representation enables constraint handling, additional variables, and non-smooth forces to be abstracted away from the upper-level optimizer, and allows classical unconstrained optimizers to synthesize trajectories for more complex systems. We provide a path-following method for efficient evaluation of constrained dynamics and utilize the implicit-function theorem to compute smooth gradients of this representation. We demonstrate the framework by modeling systems from locomotion, aerospace, and manipulation domains including: acrobot with joint limits, cart-pole subject to Coulomb friction, Raibert hopper, rocket landing with thrust limits, and planar-push task with optimization-based dynamics and then optimize trajectories using iterative LQR.
A common strategy today to generate efficient locomotion movements is to split the problem into two consecutive steps: the first one generates the contact sequence together with the centroidal trajectory, while the second one computes the whole-body trajectory that follows the centroidal pattern. Yet the second step is generally handled by a simple program such as an inverse kinematics solver. In contrast, we propose to compute the whole-body trajectory by using a local optimal control solver, namely Differential Dynamic Programming (DDP). Our method produces more efficient motions, with lower forces and smaller impacts, by exploiting the Angular Momentum (AM). With this aim, we propose an original DDP formulation exploiting the Karush-Kuhn-Tucker constraint of the rigid contact model. We experimentally show the importance of this approach by executing large steps walking on the real HRP-2 robot, and by solving the problem of attitude control under the absence of external forces.
We present a general approach for controlling robotic systems that make and break contact with their environments: linear contact-implicit model-predictive control (LCI-MPC). Our use of differentiable contact dynamics provides a natural extension of linear model-predictive control to contact-rich settings. The policy leverages precomputed linearizations about a reference state or trajectory while contact modes, encoded via complementarity constraints, are explicitly retained, resulting in policies that can be efficiently evaluated while maintaining robustness to changes in contact timings. In many cases, the algorithm is even capable of generating entirely new contact sequences. To enable real-time performance, we devise a custom structure-exploiting linear solver for the contact dynamics. We demonstrate that the policy can respond to disturbances by discovering and exploiting new contact modes and is robust to model mismatch and unmodeled environments for a collection of simulated robotic systems, including: pushbot, hopper, quadruped, and biped.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
