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Register a new userContact-Rich Trajectory Generation in Confined Environments Using Iterative Convex Optimization
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Added by
Weiye Zhao
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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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.
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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.
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.
For aerial swarms, navigation in a prescribed formation is widely practiced in various scenarios. However, the associated planning strategies typically lack the capability of avoiding obstacles in cluttered environments. To address this deficiency, we present an optimization-based method that ensures collision-free trajectory generation for formation flight. In this paper, a novel differentiable metric is proposed to quantify the overall similarity distance between formations. We then formulate this metric into an optimization framework, which achieves spatial-temporal planning using polynomial trajectories. Minimization over collision penalty is also incorporated into the framework, so that formation preservation and obstacle avoidance can be handled simultaneously. To validate the efficiency of our method, we conduct benchmark comparisons with other cutting-edge works. Integrated with an autonomous distributed aerial swarm system, the proposed method demonstrates its efficiency and robustness in real-world experiments with obstacle-rich surroundings. We will release the source code for the reference of the community.
Online state-time trajectory planning in highly dynamic environments remains an unsolved problem due to the unpredictable motions of moving obstacles and the curse of dimensionality from the state-time space. Existing state-time planners are typically implemented based on randomized sampling approaches or path searching on discretized state graph. The smoothness, path clearance, and planning efficiency of these planners are usually not satisfying. In this work, we propose a gradient-based planner over the state-time space for online trajectory generation in highly dynamic environments. To enable the gradient-based optimization, we propose a Timed-ESDT that supports distance and gradient queries with state-time keys. Based on the Timed-ESDT, we also define a smooth prior and an obstacle likelihood function that is compatible with the state-time space. The trajectory planning is then formulated to a MAP problem and solved by an efficient numerical optimizer. Moreover, to improve the optimality of the planner, we also define a state-time graph and then conduct path searching on it to find a better initialization for the optimizer. By integrating the graph searching, the planning quality is significantly improved. Experiment results on simulated and benchmark datasets show that our planner can outperform the state-of-the-art methods, demonstrating its significant advantages over the traditional ones.
As robots move from the laboratory into the real world, motion planning will need to account for model uncertainty and risk. For robot motions involving intermittent contact, planning for uncertainty in contact is especially important, as failure to successfully make and maintain contact can be catastrophic. Here, we model uncertainty in terrain geometry and friction characteristics, and combine a risk-sensitive objective with chance constraints to provide a trade-off between robustness to uncertainty and constraint satisfaction with an arbitrarily high feasibility guarantee. We evaluate our approach in two simple examples: a push-block system for benchmarking and a single-legged hopper. We demonstrate that chance constraints alone produce trajectories similar to those produced using strict complementarity constraints; however, when equipped with a robust objective, we show the chance constraints can mediate a trade-off between robustness to uncertainty and strict constraint satisfaction and also reduce the solve time compared to using the robust cost alone. Thus, our study may represent an important step towards reasoning about contact uncertainty in motion planning.
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