43 research outputs found
Contact-Implicit Trajectory Optimization Based on a Variable Smooth Contact Model and Successive Convexification
In this paper, we propose a contact-implicit trajectory optimization (CITO)
method based on a variable smooth contact model (VSCM) and successive
convexification (SCvx). The VSCM facilitates the convergence of gradient-based
optimization without compromising physical fidelity. On the other hand, the
proposed SCvx-based approach combines the advantages of direct and shooting
methods for CITO. For evaluations, we consider non-prehensile manipulation
tasks. The proposed method is compared to a version based on iterative linear
quadratic regulator (iLQR) on a planar example. The results demonstrate that
both methods can find physically-consistent motions that complete the tasks
without a meaningful initial guess owing to the VSCM. The proposed SCvx-based
method outperforms the iLQR-based method in terms of convergence, computation
time, and the quality of motions found. Finally, the proposed SCvx-based method
is tested on a standard robot platform and shown to perform efficiently for a
real-world application.Comment: Accepted for publication in ICRA 201
Contact-Implicit Trajectory Optimization using an Analytically Solvable Contact Model for Locomotion on Variable Ground
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.Comment: in IEEE Robotics and Automation Letter
Exact and Approximate Relaxation Techniques for Computational Guidance
The focus of this dissertation is in the development and application of relaxation techniques that enable efficient and real-time solution of complex computational guidance problems. Relaxations transform a non-convex constraint into a convex constraint and provides proof that the optimal solutions to the relaxed problem are optimal for the original problem. Unique contributions of this work include: 1) a relaxation technique for solving fixed final time problems between fixed points, 2) a performance analysis on the application of computational guidance for the Mars Ascent Vehicle, and 3) establishment of sufficient conditions for non-singularity of optimal control for problems on a smooth manifold with mixed constraints. The first result states that for annularly constrained linear systems, controllability is a sufficient condition for the problem to be solvable as a sequence of convex programs. The second result applies relaxations to an ascent problem. The third result is the most general result to date for problems with mixed constraints. It uses a minimum principle on manifolds with mixed constraints to analyze the problem in a geometric framework, and shows that strong observability of the dual system is sufficient for non-singularity
Numerical Solution of Optimal Control Problems with Explicit and Implicit Switches
This dissertation deals with the efficient numerical solution of switched optimal control problems whose dynamics may coincidentally be affected by both explicit and implicit switches. A framework is being developed for this purpose, in which both problem classes are uniformly converted into a mixed–integer optimal control problem with combinatorial constraints. Recent research results relate this problem class to a continuous optimal control problem with vanishing constraints, which in turn represents a considerable subclass of an optimal control problem with equilibrium constraints. In this thesis, this connection forms the foundation for a numerical treatment.
We employ numerical algorithms that are based on a direct collocation approach and require, in particular, a highly accurate determination of the switching structure of the original problem. Due to the fact that the switching structure is a priori unknown in general, our approach aims to identify it successively. During this process, a sequence of nonlinear programs, which are derived by applying discretization schemes to optimal control problems, is solved approximatively. After each iteration, the discretization grid is updated according to the currently estimated switching structure.
Besides a precise determination of the switching structure, it is of central importance to estimate the global error that occurs when optimal control problems are solved numerically. Again, we focus on certain direct collocation discretization schemes and analyze error contributions of individual discretization intervals. For this purpose, we exploit a relationship between discrete adjoints and the Lagrange multipliers associated with those nonlinear programs that arise from the collocation transcription process. This relationship can be derived with the help of a functional analytic framework and by interrelating collocation methods and
Petrov–Galerkin finite element methods. In analogy to the dual-weighted residual methodology for Galerkin methods, which is well–known in the partial differential equation community, we then derive goal–oriented global error estimators. Based on those error estimators, we present mesh refinement strategies that allow for an equilibration and an efficient reduction of the global error. In doing so we note that the grid adaption processes with respect to both switching structure detection and global error reduction get along with each other. This allows us to distill an iterative solution framework.
Usually, individual state and control components have the same polynomial degree if they originate from a collocation discretization scheme. Due to the special role which some control components have in the proposed solution framework it is desirable to allow varying polynomial degrees. This results in implementation problems, which can be solved by means of clever structure exploitation techniques and a suitable permutation of variables and equations. The resulting algorithm was developed in parallel to this work and implemented in a software package.
The presented methods are implemented and evaluated on the basis of several benchmark problems. Furthermore, their applicability and efficiency is demonstrated.
With regard to a future embedding of the described methods in an online optimal control context and the associated real-time requirements, an extension of the well–known multi–level iteration schemes is proposed. This approach is based on the trapezoidal rule and, compared to a full evaluation of the involved Jacobians, it significantly reduces the computational costs in case of sparse data matrices
Optimization-based multi-contact motion planning for legged robots
For legged robots, generating dynamic and versatile motions is essential for interacting with complex and ever-changing environments. So far, robots that routinely
operate reliably over rough terrains remains an elusive goal. Yet the primary
promise of legged locomotion is to replace humans and animals in performing
tedious and menial tasks, without requiring changes in the environment as wheeled
robots do.
A necessary step towards this goal is to endow robots with capabilities to reason
about contacts but this vital skill is currently missing. An important justification
for this is that contact phenomena are inherently non-smooth and non-convex. As a
result, posing and solving problems involving contacts is non-trivial. Optimization-based motion planning constitutes a powerful paradigm to this end. Consequently,
this thesis considers the problem of generating motions in contact-rich situations.
Specifically, we introduce several methods that compute dynamic and versatile
motion plans from a holistic optimization perspective based on trajectory optimization techniques. The advantage is that the user needs to provide a high-level
task description in the form of an objective function only. Subsequently, the
methods output a detailed motion plan—that includes contact locations, timings,
gait patterns—that optimally achieves the high-level task.
Initially, we assume that such a motion plan is available, and we investigate the
relevant control problem. The problem is to track a nominal motion plan as
close as possible given external disturbances by computing inputs for the robot.
Thus, this stage typically follows the motion planning stage. Additionally, this
thesis presents methods that do not necessarily require a separate control stage
by computing the controller structure automatically.
Afterwards, we proceed to the main parts of this thesis. First, assuming a
pre-specified contact sequence, we formulate a trajectory optimization method
reminiscent of hybrid approaches. Its backbone is a high-accuracy integrator,
enabling reliable long-term motion planning while satisfying both translational
and rotational dynamics. We utilize it to compute motion plans for a hopper
traversing rough terrains—with gaps and obstacles—and performing explosive
motions, like a somersault. Subsequently, we provide a discussion on how to
extend the method when the contact sequence is unspecified.
In the next chapter, we increase the complexity of the problem in many aspects.
First, we formulate the problem in joint-level utilizing full dynamics and kinematics
models. Second, we assume a contact-implicit perspective, i.e. decisions about
contacts are implicitly defined in the problem’s formulation rather than defined as
explicit contact modes. As a result, pre-specification of the contact interactions is
not required, like the order by which the feet contact the ground for a quadruped
robot model and the respective timings. Finally, we extend the classical rigid
contact model to surfaces with soft and slippery properties. We quantitatively
evaluate our proposed framework by performing comparisons against the rigid
model and an alternative contact-implicit framework. Furthermore, we compute
motion plans for a high-dimensional quadruped robot in a variety of terrains
exhibiting the enhanced properties.
In the final study, we extend the classical Differential Dynamic Programming
algorithm to handle systems defined by implicit dynamics. While this can be of
interest in its own right, our particular application is computing motion plans in
contact-rich settings. Compared to the method presented in the previous chapter,
this formulation enables experiencing contacts with all body parts in a receding
horizon fashion, albeit with limited contact discovery capabilities. We demonstrate
the properties of our proposed extension by comparing implicit and explicit models
and generating motion plans for a single-legged robot with multiple contacts both
for trajectory optimization and receding horizon settings.
We conclude this thesis by providing insights and limitations of the proposed
methods, and possible future directions that can improve and extend aspects of
the presented work
A Holistic Approach to Human-Supervised Humanoid Robot Operations in Extreme Environments
Nuclear energy will play a critical role in meeting clean energy targets worldwide. However, nuclear environments are dangerous for humans to operate in due to the presence of highly radioactive materials. Robots can help address this issue by allowing remote access to nuclear and other highly hazardous facilities under human supervision to perform inspection and maintenance tasks during normal operations, help with clean-up missions, and aid in decommissioning. This paper presents our research to help realize humanoid robots in supervisory roles in nuclear environments. Our research focuses on National Aeronautics and Space Administration (NASA’s) humanoid robot, Valkyrie, in the areas of constrained manipulation and motion planning, increasing stability using support contact, dynamic non-prehensile manipulation, locomotion on deformable terrains, and human-in-the-loop control interfaces
Comparison of direct and indirect methods for minimum lap time optimal control problems
Minimum lap time simulations are especially important in the design, optimisation and setup of race vehicles. Such problems usually come in different flavours, e.g. quasi-steady state models vs full dynamic models and pre-defined (fixed) trajectory problems vs free trajectory problems. This work is focused on full dynamic models with free trajectory. Practical solution techniques include direct methods (i.e. solution of an NLP problem, widespread approach) and indirect method (i.e. based on Pontryagins principle, less common, yet quite efficient in some cases). In this contribution the performance of the direct and indirect methods are compared in a number of vehicle related problems